Question 11 Mark
Express the number appearing in the statement in standard form. The earth has $1,353,000,000$ cubic km of sea water.
AnswerGiven that,
Area of sea water on earth $=1,353,000,000$ cubic km
Thus, it can be expressed in standard form as,
$1,353,000,000=1.353 \times 10^9$ cubic km
View full question & answer→Question 21 Mark
Express the number appearing in the statement in standard form: $60,230, 000,000,000,000,000,000$ molecules are contained in a drop of water weighting $1.8 gm.$
AnswerGiven that,
Total number of molecules in a drop of water weighing $1.8$ gram $= 60, 230, 000, 000, 000, 000, 000, 000 m$
Thus,
$60,230,000,000,000,000,000,000=6023 \times 10^{19}$ or, $6.023 \times 10^{22}$
View full question & answer→Question 31 Mark
Express the number appearing in the statement in standard form: The universe is estimated to be about $12,000,000,000$ years old.
AnswerEstimated age of universe $= 12, 000, 000, 000$ years
Thus, it can be expressed as,
$12,000,000,000=1.2 \times 10^{10}$ years
View full question & answer→Question 41 Mark
Express the number appearing in a statement in standard form. In a galaxy, there are on an average $100,000,000,000$ stars.
AnswerGiven that,
Average number of stars in galaxy $= 100, 000, 000, 000$ stars
Thus, it can be expressed as,
$100,000,000,000=1 \times 10^{11}$ stars
View full question & answer→Question 51 Mark
Express the number appearing in the following statements in standard form. Diameter of the Sun is $1,400,000,000 m.$
AnswerGiven that,
Diameter of Sun $= 1, 400, 000, 000 m$
Thus, it can be expressed as,
$1,400,000,000=1.4 \times 10^9 \mathrm{~m}$
View full question & answer→Question 61 Mark
Express the number appearing in the statement in standard form. Diameter of the Earth is $1,27,56,000 m.$
AnswerGiven that,
Diameter of Earth $= 1, 27, 56, 000 m$
Thus it can be expressed as,
$1,27,56,000=12756 \times 10^3 \mathrm{~m}$
$=1.2756 \times 10^7 \mathrm{~m}$
View full question & answer→Question 71 Mark
Express the number appearing in a statement in standard form. Speed of light in vacuum is $300,000,000 m/s.$
AnswerGiven that, Speed of light in vacuum $= 300, 000, 000 m/s$
Thus,
$300,000,000=3 \times 10^8 \mathrm{~m} / \mathrm{s}$
View full question & answer→Question 81 Mark
Express the number appearing in the statement in standard form: The population of India was about $1,027,000,000$ in March $2001.$
AnswerGiven that,
Population of India in March $2001= 1, 027, 000, 000$
Thus, it can be expressed as,
$1,027,000,000=1.027 \times 10^9$
View full question & answer→Question 91 Mark
Express the number appearing in the statement in standard form. The distance between Earth and Moon is $384,000,000 m.$
AnswerIt is given that,
Distance between Earth and Moon $=384,000,000 \mathrm{~m}$
Thus,
$384,000,000=3.84 \times 10^8 \mathrm{~m}$
View full question & answer→Question 101 Mark
Express the number in standard form: $3908.78$
Answer$3908.78=3.90878 \times 10^3$
View full question & answer→Question 111 Mark
Express the number in standard form: $39087.8$
Answer$39087.8=3.90878 \times 10^4$
View full question & answer→Question 121 Mark
Express the number in standard form: $3,90,878$
Answer$3,90,878=3.90878 \times 10^5$
View full question & answer→Question 131 Mark
Express the number in standard form: $3,18,65,00,000$
Answer$3,18,65,00,000=3.1865 \times 10^9$
View full question & answer→Question 141 Mark
Express the number in standard form: $70,00,000$
Answer$70,00,000=7.0 \times 10^6$
View full question & answer→Question 151 Mark
Express the number in standard form: $5,00,00,000$
Answer$5,00,00,000=5.0 \times 10^7$
View full question & answer→Question 161 Mark
Find the number from the expanded form: $9 \times 10^5+2 \times 10^2+3 \times 10^1$
Answer$9 \times 10^5+2 \times 10^2+3 \times 10^1=900230$
$900000+00000+0000+200+30=900230$
View full question & answer→Question 171 Mark
Find the number from the expanded form: $3 \times 10^4+7 \times 10^2+5 \times 10^0$
Answer$3 \times 10^4+7 \times 10^2+5 \times 10^0=30705$
$30000+0000+700+00+5=30705$
View full question & answer→Question 181 Mark
Find the number from the expanded form: $4 \times 10^5+5 \times 10^3+3 \times 10^2+2 \times 10^0$
Answer$4 \times 10^5+5 \times 10^3+3 \times 10^2+2 \times 10^0=405302$
$400000+00000+5000+300+00+2=405302$
View full question & answer→Question 191 Mark
Find the number from the expanded form: $8 \times 10^4+6 \times 10^3+0 \times 10^2+4 \times 10^1+5 \times 10^0$
Answer$8 \times 10^4+6 \times 10^3+0 \times 10^2+4 \times 10^1+5 \times 10^0=86045$
$80000+6000+000+40+5=86045$
View full question & answer→Question 201 Mark
Write the number in expanded form: $20068$
Answer$20068=2 \times 10000+0 \times 1000+0 \times 100+6 \times 10+8 \times 1$
$=2 \times 10^4+0 \times 10^3+0 \times 10^2+6 \times 10^1+8 \times 10^0$
View full question & answer→Question 211 Mark
Write the number in expanded form: $120719$
Answer$120719=1 \times 100000+2 \times 10000+0 \times 1000+7 \times 100+1 \times 10+9 \times 1$
$=1 \times 10^5+2 \times 10^4+0 \times 10^3+7 \times 10^2+1 \times 10^1+9 \times 10^0$
View full question & answer→Question 221 Mark
Write the number in expanded forms: $2806196$
Answer$2806196=2 \times 1000000+8 \times 100000+0 \times 10000+6 \times 1000+1 \times 100+9 \times 10+6 \times 1$
$=2 \times 10^6+8 \times 10^5+0 \times 10^4+6 \times 10^3+1 \times 10^2+9 \times 10^1+6 \times 10^0$
View full question & answer→Question 231 Mark
Write the number in expanded form: $3006194$
Answer$3006194=3 \times 1000000+0 \times 100000+0 \times 10000+6 \times 1000+1 \times 100+9 \times 10+4 \times 1$
$=3 \times 10^6+0 \times 10^5+0 \times 10^4+6 \times 10^3+1 \times 10^2+9 \times 10^1+4 \times 10^0$
View full question & answer→Question 241 Mark
Write the number in expanded form: 279404
Answer$279404=2 \times 100000+7 \times 10000+9 \times 1000+4 \times 100+0 \times 10+4 \times 1$
$=2 \times 10^5+7 \times 10^4+9 \times 10^3+4 \times 10^2+0 \times 10^1+4 \times 10^0$
View full question & answer→Question 251 Mark
Using laws of exponents, simplify and write the answer in exponential form $\left(3^4\right)^3$
AnswerWe have,
$\left(3^4\right)^3$
We know that, $\left(a^m\right)^n=a^{m n}$
Thus,
$\left(3^4\right)^3=3^{4 \times 3}=3^{12}$
View full question & answer→Question 261 Mark
Using laws of exponents, simplify and write the answer in exponential form $7^x \times 7^2$
AnswerHere,
$7^x \times 7^2$
We know that, $a^m \times a^n=a^{m+n}$
Thus,
$7^x \times 7^2=(7)^{x+2}$
View full question & answer→Question 271 Mark
Using laws of exponent, simplify and write the answer in exponential form: $a^3 \times a^2$
AnswerBy the law of exponents, $x^m \times x^n=x^{m+n}$
By applying this law, $a^3 \times a^2=a^{3+2}=a^5$
Hence $a^3 \times a^2=a^5$
View full question & answer→Question 281 Mark
Using laws of exponent, simplify and write the answer in exponential form: $8^t \div 8^2$
AnswerBy the law of exponenets we have $x^m \div x^n=x^{m-n}$
By applying this law, $8^{\mathrm{t}} \div 8^2=8^{\mathrm{t}-2}$
View full question & answer→Question 291 Mark
Simplify: $(-3) \times(-2)^3$
AnswerIn order to find $(-2)^3$, we should multiply $(-2) 3$ times
$(-2)^3=(-2) \times(-2) \times(-2)=(-8)$
$(-3) \times(-2)^3=(-3) \times(-8)=24$
View full question & answer→Question 301 Mark
Simplify: $(-4)^3$
AnswerHere,
$(-4)^3$
$=(-4) \times(-4) \times(-4)$
$=-64$
View full question & answer→Question 311 Mark
Simplify: $3^2 \times 10^4$
AnswerWe have, $3^2 \times 10^4=3 \times 3 \times 10 \times 10 \times 10 \times 10=9 \times 10000=90000$
View full question & answer→Question 321 Mark
Simplify: $2^4 \times 3^2$
AnswerIn order to find $2^4$, we should multiply $2$ four times
$2^4=2 \times 2 \times 2 \times 2=16$
In order to find $3^2$, we should multiply $3$ two times
$3^2=3 \times 3=9$
$2^4 \times 3^2=16 \times 9=144$
$2^4 \times 3^2=144$
View full question & answer→Question 331 Mark
Simplify: $5^2 \times 3^3$
AnswerTo find $5^2$, multiply $5$ , two times
$5^2=5 \times 5=25$
To find $3^3$, multiply $3$ , three times
$3^3=3 \times 3 \times 3=27$
Hence, $5^2 \times 3^3=25 \times 27=675$
View full question & answer→Question 341 Mark
Simplify: $0 \times 10^2$
AnswerAny number multiplied by $'0'$ is $'0'$, however big the number is
Hence, $0 \times 10^2 = 0$
View full question & answer→Question 351 Mark
Simplify: $3 \times 4^4$
AnswerHere,
$3 \times 4^4$
$=3 \times 4 \times 4 \times 4 \times 4$
$=3 \times 256$
$=768$
View full question & answer→Question 361 Mark
Simplify: $2^3 \times 5$
AnswerIn order to get $2^3$, multiply $2$ three times
$2^3=2 \times 2 \times 2=8$
$2^3 \times 5=8 \times 5=40$
View full question & answer→Question 371 Mark
Simplify: $7^2 \times 2^2$
AnswerIn order to get $7^2$, multiply $7$ two times
$7^2=7 \times 7=49$
In order to get $2^2$, multiply $2$ two times
$2^2=2 \times 2=4$
Hence $7^2 \times 2^2=49 \times 4=196$
View full question & answer→Question 381 Mark
Simplify: $2 \times 10^3$
AnswerTo expand $10^3$, multiply $10$ three times
$10^3=10 \times 10 \times 10=1000$
$2 \times 10^3=2 \times 1000=2000$
View full question & answer→Question 391 Mark
Express the number as a product of power of its prime factors: $405$
AnswerTo get the prime factors, divide the number $405$ with the prime numbers
$\therefore 405=3 \times 3 \times 3 \times 3 \times 5=3^4 \times 5$
It is the required prime factor product form. View full question & answer→Question 401 Mark
Identify the greater number, if possible: $2^{10}$ or $10^2$
AnswerIn order to find the greater number, we should expand and find the value of $2^{10}$ and $10^2$
$2^{10}=2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2=1024$
$10^2=10 \times 10=100$
Since $1024>100,2^{10}>10^2$
View full question & answer→Question 411 Mark
Express the number using exponential notation: $3125$
Answer$3125$
We have,
$3125=5 \times 5 \times 5 \times 5 \times 5=5^5$ View full question & answer→Question 421 Mark
Express the number using the exponential notation: $343$
AnswerIn order to express $343$ in exponential notation, we should find the prime factors of $343$ and express $343$ as the product of its prime factors
$\therefore 343=7 \times 7 \times 7=7^3$ View full question & answer→Question 431 Mark
Express in exponential form: $a \times a \times a \times c \times c \times c \times c \times d$
AnswerWe have,
$a \times a \times a \times c \times c \times c \times c \times d$
$=a^{1+1+1} \times c^{1+1+1+1} \times d^1$ [Bases are same, powers are added]
$=a^3 \times c^4 \times d$
View full question & answer→Question 441 Mark
Express in exponential form: $2 \times 2 \times a \times a$
AnswerWe have,
$2 \times 2 \times a \times a$
$=2^{1+1} \times a^{1+1}$[ Bases are same, powers are added]
$=2^2 \times a^2$
View full question & answer→Question 451 Mark
Express in exponential form: $5 \times 5 \times 7 \times 7 \times 7$
AnswerWe have,
$5 \times 5 \times 7 \times 7 \times 7$
$=5^{1+1} \times 7^{1+1+1}$ [Bases are same, powers are added]
$=5^2 \times 7^3$
View full question & answer→Question 461 Mark
Express in exponential form: $b \times b \times b \times b$
AnswerWe have,
$b \times b \times b \times b$
$=b^{1+1+1+1}$ [Bases are same, powers are added]
$=b^4$
View full question & answer→Question 471 Mark
Express in exponential form: $t \times t$
AnswerWe have,
$t \times t$
$=t^{1+1}$ [Bases are same, powers are added]
$=t^2$
View full question & answer→Question 481 Mark
Express in exponential form: $6 \times 6 \times 6 \times 6$
AnswerWe have,
$6 \times 6 \times 6 \times 6$
$=6^{1+1+1+1} $ [Bases are same, powers are added]
$=6^4$
View full question & answer→Question 491 Mark
Find the value of $5^4$
AnswerIn order to get the value of $5^4$, we should multiply $5, 4$ timesHence $5^4=5 \times 5 \times 5 \times 5=625$.
View full question & answer→Question 501 Mark
Find the value of $11^2$
AnswerIn order to find the value $11^2$, multiply $11,2$ timesHence $11^2=11 \times 11=121$
View full question & answer→Question 511 Mark
Find the value of $9^3$
AnswerIn order to get the value of $9^3$, we should multiply $9$ three timesHence, $9^3=9 \times 9 \times 9=729$
View full question & answer→Question 521 Mark
Find the value of $2^6$
AnswerIn order to get the value of $2^6$, we should multiply $2$ six timesHence $2^6=2 \times 2 \times 2 \times 2 \times 2 \times 2=64$
View full question & answer→Question 531 Mark
Expand: $\left(\frac{-4}{7}\right)^{5}$
AnswerHere, $\left(\frac{-4}{7}\right)^{5}=\frac{(-4)^{5}}{7^{5}}$ $=\frac{(-4) \times(-4) \times(-4) \times(-4) \times(-4)}{7 \times 7 \times 7 \times 7 \times 7}$
View full question & answer→Question 541 Mark
Expand: $\left(\frac{3}{5}\right)^{4}$
AnswerHere, $\left(\frac{3}{5}\right)^{4}=\frac{3^{4}}{5^{4}}=\frac{3 \times 3 \times 3 \times 3}{5 \times 5 \times 5 \times 5}$
View full question & answer→Question 551 Mark
Can you tell which one is greater $\left(5^2\right) \times 3$ or $\left(5^2\right)^3 $?
Answer$\left(5^2\right) \times 3$ means $5^2$ is multiplied by $3$ i.e., $5 \times 5 \times 3=75$
but $\left(5^2\right)^3$ means $5^2$ is multiplied by itself three times i.e..
$5^2 \times 5^2 \times 5^2=5^6=15,625$
Therefore $\left(5^2\right)^3>\left(5^2\right) \times 3$
View full question & answer→Question 561 Mark
Which one is greater $2^3$ or $3^2$?
AnswerHere,
$2^3=2 \times 2 \times 2=8 \text { and }$
$3^2=3 \times 3=9$
Since $9>8$,
So, $3^2$ is greater than $2^3$
View full question & answer→Question 571 Mark
Express the number in the standard form: $70,040,000,000$
Answer$70,040,000,000=7.004 \times 10,000,000,000=7.004 \times 10^{10}$
View full question & answer→Question 581 Mark
Express the number in the standard form: $3,430,000$
Answer$3,430,000=3.43 \times 1,000,000=3.43 \times 10^6$
View full question & answer→Question 591 Mark
Express the number in the standard form: $65,950$
AnswerHere, $65,950=6.595 \times 10,000=6.595 \times 10^4$
View full question & answer→Question 601 Mark
Express the number in the standard form: $5985.3$
AnswerHere, $5985.3=5.9853 \times 1000=5.9853 \times 10^3$
View full question & answer→Question 611 Mark
Simplify: $2^3 \times a^3 \times 5 a^4$
AnswerHere,
$2^{3} \times a^{3} \times 5 a^{4}$
= $2^{3} \times a^{3} \times 5 \times a^{4}$
= $2^{3} \times 5 \times a^{3} \times a^{4}$
= $8 \times 5 \times a^{3+4}$
= $40a^7$
View full question & answer→Question 621 Mark
Simplify and write the answer in the exponential form: $8^2 \div 2^3$
AnswerHere, $8=2 \times 2 \times 2=2^3$
Thus, $8^2 \div 2^3=\left(2^3\right)^2 \div 2^3$
$=2^6 \div 2^3=2^{6-3}=2^3$
View full question & answer→Question 631 Mark
Simplify and write the answer in the exponential form: $\left[\left(2^2\right)^3 \times 3^6\right] \times 5^6$
AnswerHere,
${\left[\left(2^2\right)^3 \times 3^6\right] \times 5^6}$
$=\left[2^6 \times 3^6\right] \times 5^6$
$=(2 \times 3)^6 \times 5^6$
$=(2 \times 3 \times 5)^6=30^6$
View full question & answer→Question 641 Mark
Simplify and write the answer in the exponential form: $\left(6^2 \times 6^4\right) \div 6^3$
AnswerHere,
$\left(6^{2} \times 6^{4}\right) \div 6^{3}$
= $6^{2+4} \div 6^{3}$
$=\frac{6^{6}}{6^{3}}=6^{6-3}=6^{3}$
View full question & answer→Question 651 Mark
Simplify and write the answer in the exponential form: $2^3 \times 2^2 \times 5^5$
Answer$\text { Here, } 2^3 \times 2^2 \times 5^5$
$=2^{3+2} \times 5^5$
$=2^5 \times 5^5$
$=(2 \times 5)^5$
$=10^5$
View full question & answer→Question 661 Mark
Simplify and write the answer in the exponential form: $\left(\frac{3^{7}}{3^{2}}\right) \times 3^{5}$
AnswerHere, $\left(\frac{3^{7}}{3^{2}}\right) \times 3^{5}=\left(3^{7-2}\right) \times 3^{5}$
$=3^5 \times 3^5$
$=3^{5+5}$
$=3^{10}$
View full question & answer→Question 671 Mark
Express $256$ as a power $2.$
AnswerGiven number is, $256$
It can be expressed as,
$256=2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \text {. }$
So we can say that $256=2^8$
View full question & answer→