Question 11 Mark
Express of the following numbers as a product of powers of thier prime factors:
$24000$
Answer$24000=2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 5 \times 5 \times 5$
$=2^5 \times 3 \times 5^3$
View full question & answer→Question 21 Mark
Identify the greater number in the following:
$2^5 \text { or } 5^2$
Answer$2^5 \text { or } 5^2$
$=2^5=2 \times 2 \times 2 \times 2 \times 2$
$=32$
$=5^2=5 \times 5$
$=25$
Therefore, $2^5, 5^2$
View full question & answer→Question 31 Mark
If $a = 2$ and $b = 3$, the find the values of the following: $\Big(\frac{\text{a}}{\text{b}}+\frac{\text{b}}{\text{a}}\Big)^{\text{a}}$
Answer$\Big(\frac{\text{a}}{\text{b}}+\frac{\text{b}}{\text{a}}\Big)^{\text{a}}=\Big(\frac{\text{2}}{\text{3}}+\frac{\text{3}}{\text{2}}\Big)^{\text{2}}$ $=\frac{169}{36}$
View full question & answer→Question 41 Mark
Express the following in exponential form:
$\mathrm{x} \times \mathrm{x} \times \mathrm{x} \times \mathrm{x} \times \mathrm{a} \times \mathrm{a} \times \mathrm{b} \times \mathrm{b} \times \mathrm{b}$
Answer$\mathrm{x} \times \mathrm{x} \times \mathrm{x} \times \mathrm{x} \times \mathrm{a} \times \mathrm{a} \times \mathrm{b} \times \mathrm{b} \times \mathrm{b}$
$=x^4 a^2 b^3$
View full question & answer→Question 51 Mark
Express the following numbers in the standard form:
$3,18,65,00,000$
Answer$3,18,65,00,000 = 3,18,65,00,000.00$
$=3.1865 \times 10^9$
Since, the decimal point is moved nine places to the left
View full question & answer→Question 61 Mark
Simply: $(-2)^5 \times(-10)^2$
Answer$(-2)^5 \times(-10)^2=(-2) \times(-2) \times(-2) \times(-2) \times(-2) \times(-10) \times(-10)$
$=(-32) \times 100$
$=-3200$
View full question & answer→Question 71 Mark
Write the following numbers in the expanded exponential forms:
$420719$
Answer$420719=4 \times 10^5+2 \times 10^4+0 \times 10^3+7 \times 10^2+1 \times 10^1+9 \times 10^0$
View full question & answer→Question 81 Mark
Simply:
$\Big(\frac{3}{4}\Big)^2$
Answer $\Big(\frac{3}{4}\Big)^2=\frac{3\times3}{4\times4}$
$=\frac{9}{16}$
View full question & answer→Question 91 Mark
Write the following numbers in the expanded exponential forms:
$927303$
AnswerWe have:
$927303=9 \times 10^5+2 \times 10^4+7 \times 10^3+3 \times 10^2+0 \times 10^1+3 \times 10^0$
Note: $a^0=1$
View full question & answer→Question 101 Mark
Express the following rational numbers in power notation: $\frac{49}{64}$
Answer$\frac{49}{64}=\Big(\frac{7}{8}\Big)^2$ Because $7^2 = 49$ and $8^2 = 64$
View full question & answer→Question 111 Mark
Express the numbers appearing in the following statements in the standard form:
Diameter of the sun is $1, 400, 000, 000$ metres.
AnswerDiameter of the sun is $1.4 \times 10^9$ metres.
Since, the decimal point is moved nine places to the left.
View full question & answer→Question 121 Mark
Write the following numbers in the usual form:
$3.5 \times 10^3$
Answer$3.5 \times 10^3=35 \times 10^{(3-1)}$
$=35 \times 10^2$
$=3,500$
View full question & answer→Question 131 Mark
Find the values of the following: $7^3$
Answer$7^3 = 7 × 7 × 7$
$= 343$
View full question & answer→Question 141 Mark
Express the following in exponential form:
$\Big(\frac{4}{3}\times\frac{4}{3}\times\frac{4}{3}\times\frac{4}{3}\times\frac{4}{3}\Big)$
Answer $\Big(\frac{4}{3}\times\frac{4}{3}\times\frac{4}{3}\times\frac{4}{3}\times\frac{4}{3}\Big)$
$=\Big(\frac{4}{3}\Big)^5$
View full question & answer→Question 151 Mark
Simply: $\Big(\frac{-2}{3}\Big)^2$
Answer$\Big(\frac{-2}{3}\Big)^4=\frac{(-2)\times(-2)\times(-2)\times(-2)}{3\times3\times3\times3}$ $=\frac{16}{81}$
View full question & answer→Question 161 Mark
Find the values of the following: $2^4 \times 3^2$
Answer$ 2^4 \times 3^2=2 \times 2 \times 2 \times 2 \times 3 \times 3$
$=16 \times 9$
$=144$
View full question & answer→Question 171 Mark
Find the values of the following:
$3 \times 10^2$
Answer$3 \times 10^2=3 \times 10 \times 10$
$=3 \times 100$
$=300$
View full question & answer→Question 181 Mark
Identify the greater number of the following: $3^5 \text { or } 5^3$
Answer$3^5 \text { or } 5^3$
$=3^5=3 \times 3 \times 3 \times 3 \times 3$
$=243$
$=5^3=5 \times 5 \times 5$
$=125$
Therefore, $3^5, 5^3$
View full question & answer→Question 191 Mark
Find the number from the following expanded forms:
$3 \times 10^4+4 \times 10^2+5 \times 10^0$
AnswerWe have:
$3 \times 10^4+4 \times 10^2+5 \times 10^0$
$=3 \times 10000+4 \times 100+5 \times 1=30405$
View full question & answer→Question 201 Mark
Express the following in exponential form:
$36$
Answer$36=2 \times 2 \times 3 \times 3$
$=2^2 \times 3^2$
View full question & answer→Question 211 Mark
Express the following rational numbers in power notation: $-\frac{1}{216}$
Answer$-\frac{1}{216}=\Big(-\frac{1}{6}\Big)^3$ Because $1^3 = 1$ and $6^3 = 216$
View full question & answer→Question 221 Mark
Express the numbers appearing in the following statements in the standard form: The universe is estimated to be about $12,000,000,000$ years old.
AnswerThe universe is estimated to be about $1.2 \times 10^{10}$ years old.
Since, the decimal point is moved ten places to the left.
View full question & answer→Question 231 Mark
If $a = 2$ and $b = 3$, the find the values of the following:
$(a b)^b$
Answer$(a b)^b=(2 \times 3)^3$
$=(6)^3$
$=216$
View full question & answer→Question 241 Mark
Express the following numbers in the standard form:
$3908.78$
Answer$3908.78=3.90878 \times 10^3$
Since, the decimal point is moved three places to the left
View full question & answer→Question 251 Mark
If $a = 2$ and $b = 3$, the find the values of the following:$\Big(\frac{\text{b}}{\text{a}}\Big)^{\text{b}}$
Answer$\Big(\frac{\text{b}}{\text{a}}\Big)^{\text{b}}=\Big(\frac{\text{3}}{\text{2}}\Big)^{\text{3}}$$=\frac{27}{8}$
View full question & answer→Question 261 Mark
Identify the greater number in the following:
$3^4 \text { or } 4^3$
Answer$3^4 \text { or } 4^3$
$=3^4=3 \times 3 \times 3 \times 3$
$=81$
$=4^3=4 \times 4 \times 4$
$=64$
Therefore, $3^4, 4^3$
View full question & answer→Question 271 Mark
Find the values of the following:
$5^2 \times 3^4$
Answer$5^2 \times 3^4=5 \times 5 \times 3 \times 3 \times 3 \times 3$
$=25 \times 81$
$=2025$
View full question & answer→Question 281 Mark
Find the values of the following:
$5^2 \times 3^4$
Answer$3^3 \times 5^2=3 \times 3 \times 3 \times 5 \times 5$
$=27 \times 25$
$=675$
View full question & answer→Question 291 Mark
Express the numbers appearing in the following statements in the standard form:
The distance between the earth and the moon is $384,000,000$ metres.
AnswerThe distance between the earth and the moon is $3.84 \times 10^8$ metres.
Since, the decimal point is moved eight places to the left.
View full question & answer→Question 301 Mark
Find the values of the following:
$2^2 \times 5^3$
Answer$2^2 \times 5^3=2 \times 2 \times 5 \times 5 \times 5$
$=4 \times 125$
$=500$
View full question & answer→Question 311 Mark
Find the value of following: $\Big(\frac{-1}{2}\Big)^2\times2^3\times\Big(\frac{3}{4}\Big)^2$
Answer$\Big(\frac{-1}{2}\Big)^2\times2^3\times\Big(\frac{3}{4}\Big)^2$ $=\frac{1}{2}\times8\times\frac{9}{16}$ $=\frac{9}{8}$
View full question & answer→Question 321 Mark
Simply:
$(-3)^2 \times(-5)^3$
Answer$(-3)^2 \times(-5)^3=(-3) \times(-3) \times(-5) \times(-5) \times(-5)$
$=9 \times(-125)$
$=-1125$
View full question & answer→Question 331 Mark
Write the following numbers in the usual form:
$3.21 \times 10^5$
Answer$3.21 \times 10^5$
$=321 \times 10^{(5-2)}$
$=321 \times 10^3$
$=3,21,000$
View full question & answer→Question 341 Mark
Find the values of the following:
$(-3)^4$
AnswerWe know that if 'a' is natural number, then
$(-a)^{\text {even number }}=$ positive number
$(-a)^{\text {even number }}=$ negative number
We have,
$(-3)^4=(-3) \times(-3) \times(-3) \times(-3)$
$=81$
View full question & answer→Question 351 Mark
If $a=2$ and $b=3$, the find the values of the following:
$(a+b)^a$
Answer$(a+b)^a=(2+3)^2$
$=(5)^2$
$=25$
View full question & answer→Question 361 Mark
Express of the following as a rational number of the form $\frac{\text{p}}{\text{q}}$
$\Big(\frac{-2}{3}\Big)^4$
Answer $\Big(\frac{-2}{3}\Big)^4$
$=\frac{(-2)\times(-2)\times(-2)\times(-2)}{3\times3\times3\times3}$
$=\frac{16}{81}$
View full question & answer→Question 371 Mark
Simply:
$(-2) \times(-3)^3$
Answer$(-2) \times(-3)^3=(-2) \times(-3) \times(-3) \times(-3)$
$=(-2) \times(-27)$
$=54$
View full question & answer→Question 381 Mark
Express the following in exponential form:
$625$
View full question & answer→Question 391 Mark
Write the following numbers in the expanded exponential forms:
$5004132$
AnswerWe have:
$5004132=5 \times 10^6+0 \times 10^5+0 \times 10^4+4 \times 10^3+1 \times 10^2+3 \times 10^1+2 \times 10^0$
View full question & answer→MCQ 401 Mark
$(25^2-15^2)^{\frac{3}{2}}=$
- A
$4000$
- ✓
$8000$
- C
$3125$
- D
$1024$
AnswerCorrect option: B. $8000$
Since,
$(25^2-15^2)^{\frac{3}{2}}$
$=(625-225)^{\frac{3}{2}}$
$=(400)^{\frac{3}{2}}$
$=(20^2)^{\frac{3}{2}}$
$=20^{2\times\frac{3}{2}}$ $\Big[\text{As, }(\text{x}^{\text{m}})^{\text{n}}=\text{x}^{\text{mn}}\Big]$
$=20^3$
$=8000$
Hence, the correct alternative is option $(b)$.
View full question & answer→Question 411 Mark
Express the following in exponential form: $\Big(\frac{-5}{7}\times\frac{-5}{7}\times\frac{-5}{7}\times\frac{-5}{7}\Big)$
Answer$\Big(\frac{-5}{7}\times\frac{-5}{7}\times\frac{-5}{7}\times\frac{-5}{7}\Big)=\Big(\frac{-5}{7}\Big)^4$
View full question & answer→Question 421 Mark
Simply: $\Big(\frac{-4}{5}\Big)^2$
Answer$\Big(\frac{-4}{5}\Big)^4=\frac{(-4)\times(-4)\times(-4)\times(-4)}{5\times5\times5\times5\times5}$ $=\frac{-1024}{3125}$
View full question & answer→Question 431 Mark
Express of the following as a rational number of the form $\frac{\text{p}}{\text{q}}$ $\Big(\frac{7}{9}\Big)^3$
Answer$\Big(\frac{7}{9}\Big)^3$ $=\frac{7\times7\times7}{9\times9\times9}$ $=\frac{343}{729}$
View full question & answer→Question 441 Mark
Express the following in exponential form:
$392$
Answer$392=2 \times 2 \times 2 \times 7 \times 7$
$=2^3 \times 7^2$
View full question & answer→Question 451 Mark
Find the value of following: $\Big(\frac{-3}{5}\Big)^4\times\Big(\frac{4}{9}\Big)^4\times\Big(\frac{-15}{18}\Big)^2$
Answer$\Big(\frac{-3}{5}\Big)^4\times\Big(\frac{4}{9}\Big)^4\times\Big(\frac{-15}{18}\Big)^2$ $=\frac{81}{625}\times\frac{256}{6561}\times\frac{225}{324}=\frac{94}{18225}$
View full question & answer→Question 461 Mark
Express the following in exponential form: $\Big(\frac{-2}{3}\Big)\times\Big(\frac{-2}{3}\Big)\times\text{x}\times\text{x}\times\text{x}$
Answer$\Big(\frac{-2}{3}\Big)\times\Big(\frac{-2}{3}\Big)\times\text{x}\times\text{x}\times\text{x}$ $=\Big(\frac{-2}{3}\Big)^{2}\text{x}^3$
View full question & answer→Question 471 Mark
Find the values of the following: $(-7)^2$
AnswerWe know that If 'a' is natural number, then
$(-a)^{\text {even number }}=$ positive number
$(-a)^{\text {even number }}=$ negative number
We have,
$(-7)^2=(-7) \times(-7)$
$=49$
View full question & answer→Question 481 Mark
Find the values of the following:
$3^2 \times 10^4$
Answer$3^2 \times 10^4=3 \times 3 \times 10 \times 10 \times 10 \times 10$
$=9 \times 10000$
$=90000$
View full question & answer→Question 491 Mark
Find the values of the following:
$3^4$
Answer$3^4=3 \times 3 \times 3 \times 3$
$=81$
View full question & answer→Question 501 Mark
Express of the following numbers as a product of powers of thier prime factors:
$2800$
Answer$2800=2 \times 2 \times 2 \times 2 \times 5 \times 5 \times 7$
$=2^4 \times 5^2 \times 7$
View full question & answer→