Question 11 Mark
Find the reciprocal of the following: $(-4)^3$
Answer$(-4)^3=\Big(\frac{-1}{4}\Big)^3$
View full question & answer→Question 21 Mark
Fill in the blank.$(-2)^{-5}= ......$
Answer$(-2)^{-5}=\frac{-1}{32}$
$\Big[\text{Since}\Big(\frac{\text{a}}{\text{b}}\Big)^{-1}=\Big(\frac{\text{b}}{\text{a}}\Big)^1\Big]$
$(-2)^{-5}=\Big(\frac{-2}{1}\Big)^{-5}=\Big(\frac{1}{-2}\Big)^5$
$=\frac{(1)^5}{(-2)^5}=\frac{1\times1\times1\times1\times1}{(-2)\times(-2)\times(-2)\times(-2)\times(-2)}$
$=\frac{1}{-32}$
View full question & answer→Question 31 Mark
Fill in the blank. $\Big(\frac{\text{a}}{\text{b}}\Big)^{-16}=\ ...... $
Answer$\Big(\frac{\text{a}}{\text{b}}\Big)^{-16}=\Big(\frac{\text{b}}{\text{a}}\Big)^{16}$
We know, $\Big(\frac{\text{a}}{\text{b}}\Big)^{-1}=\Big(\frac{\text{b}}{\text{a}}\Big)^1$
View full question & answer→Question 41 Mark
Express the following in power notation:
$\frac{-27}{64}$
Answer $\frac{-27}{64}=\frac{(-3)\times(-3)\times(-3)}{4\times 4\times 4}$
$=\Big(\frac{-3}{4}\Big)\times \Big(\frac{-3}{4}\Big)\times \Big(\frac{-3}{4}\Big)$
$=\Big(\frac{-3}{4}\Big)^3$
View full question & answer→Question 51 Mark
Write the numeral whose expanded form is given below:
$6 \times 10^4+3 \times 10^3+0 \times 10^2+7 \times 10^1+8 \times 10^0$
Answer$6 \times 10^4+3 \times 10^3+0 \times 10^2+7 \times 10^1+8 \times 10^0$
$=60000+3000+0+70+8$
$=63078$
View full question & answer→Question 61 Mark
Write the following in power notation: $\Big(\frac{-4}{3}\Big)\times \Big(\frac{-4}{3}\Big)\times \Big(\frac{-4}{3}\Big)\times \Big(\frac{-4}{3}\Big)\times \Big(\frac{-4}{3}\Big)$
Answer$\Big(\frac{-4}{3}\Big)\times \Big(\frac{-4}{3}\Big)\times \Big(\frac{-4}{3}\Big)\times \Big(\frac{-4}{3}\Big)\times \Big(\frac{-4}{3}\Big)=\Big(\frac{-4}{3}\Big)^5$
View full question & answer→Question 71 Mark
Write the following numbers in expanded form:
$5807294$
Answer$5807294=5 \times 10^6+8 \times 10^5+0 \times 10^4+7 \times 10^3+2 \times 10^2+9 \times 10^1+4 \times 10^0$
View full question & answer→Question 81 Mark
Express the following numbers in standard form:
$940000000000$
AnswerWe can write in standard form
$940000000000=9.40000000000 \times 10^{11}$
$=9.4 \times 10^{11}$
View full question & answer→Question 91 Mark
Express the following numbers in standard form:
Diameter of Earth = $12756000m$.
Answer$\text { Diameter of Earth }=12756000 \mathrm{~m}$
$=1.2756000 \times 10^7 \mathrm{~m}$
$=1.2756 \times 10^7 \mathrm{~m}$
View full question & answer→Question 101 Mark
Write the following numbers in expanded form:
$4007185$
Answer$4007185=4 \times 10^6+0 \times 10^5+0 \times 10^4+7 \times 10^3+1 \times 10^2+8 \times 10^1+5 \times 10^0$
View full question & answer→Question 111 Mark
Fill in the blank.
$(8)^0=?$
Answer$(8)^0=\underline{1}$
By definition, we have $a^0=1$ for every integer a.
$\therefore(8)^0=1$
View full question & answer→Question 121 Mark
Express the following as a rational number: $\Big(\frac{1}{4}\Big)^{-4}$
Answer$\Big(\frac{1}{4}\Big)^{-4}=(4)^{4}$ $=4\times4\times4\times4$ $=256$
View full question & answer→Question 131 Mark
Write the following in power notation: $\frac{5}{7}\times \frac{5}{7}\times \frac{5}{7}\times\frac{5}{7}$
Answer$\frac{5}{7}\times \frac{5}{7}\times \frac{5}{7}\times\frac{5}{7}=\Big(\frac{5}{7}\Big)^4$
View full question & answer→Question 141 Mark
Write the following in power notation: $\Big(\frac{-1}{6}\Big)\times\Big(\frac{-1}{6}\Big)\times\Big(\frac{-1}{6}\Big)$
Answer$\Big(\frac{-1}{6}\Big)\times\Big(\frac{-1}{6}\Big)\times\Big(\frac{-1}{6}\Big)=\Big(\frac{-1}{6}\Big)^3$
View full question & answer→Question 151 Mark
Find the value of the following: $8^\circ $
AnswerWe know that $\Big(\frac{\text{a}}{\text{b}}\Big)^\circ=1,$
therefore $8^\circ = 1$
View full question & answer→Question 161 Mark
Write $'T'$ for true and $'F'$ for false for the following:
$\left(3^0+4^0+5^0\right)=12$.
AnswerFalse.
$\left(3^0+4^0+5^0\right)=1\left[\right.$ Since $a^0=1$ for every integer a]
View full question & answer→Question 171 Mark
Express the following numbers in standard form:
$23000000$
AnswerWe can write in standard form
$23000000=2.3000000 \times 10^7$
$=2.3 \times 10^7$
View full question & answer→Question 181 Mark
Write the following numbers in expanded form:
$684502$
Answer$684502=6 \times 10^5+8 \times 10^4+4 \times 10^3+5 \times 10^2+0 \times 10^1+2 \times 10^0$
View full question & answer→Question 191 Mark
Express the following numbers in standard form:
$538$
AnswerWe can write in standard form
$538=5.38 \times 10^2$
View full question & answer→Question 201 Mark
Express the following as a rational number: $\Big(\frac{23}{25}\Big)^\circ$
Answer$\Big(\frac{23}{25}\Big)^\circ=1$
View full question & answer→Question 211 Mark
Find the value of the following: $4^\circ + 5^\circ $
AnswerWe know that $\Big(\frac{\text{a}}{\text{b}}\Big)^\circ=1,$
therefore $4^\circ + 5^\circ = 1 + 1 = 2$
View full question & answer→Question 221 Mark
Express the following in power notation: $\frac{25}{36}$
Answer $\frac{25}{36}=\frac{5\times5}{6\times 6}$ $=\frac{5}{6}\times \frac{5}{6}$ $=\Big(\frac{5}{6}\Big)^2$
View full question & answer→Question 231 Mark
Express the following numbers in standard form: $6428000$
AnswerWe can write in standard form
$6428000=6.428000 \times 10^6$
$=6.428 \times 10^6$
View full question & answer→Question 241 Mark
Write the reciprocal of:
$(-5)^{6}$
AnswerWe know that the reciprocal of $\Big(\frac{\text{a}}{\text{b}}\Big)^\text{m}\text{ is }\Big(\frac{\text{b}}{\text{a}}\Big)^\text{m}$
Reciprocal of $(-5)^6$ = Reciprocol of $\Big(\frac{-5}{1}\Big)^6=\Big(\frac{-1}{5}\Big)^6$
View full question & answer→Question 251 Mark
Write the following in power notation:
$(-8)\times (-8)\times (-8)\times (-8)\times (-8)$
Answer $(-8)\times (-8)\times (-8)\times (-8)\times (-8)=(-8)^5$
View full question & answer→Question 261 Mark
Express the following numbers in standard form: Population of India in March $2001 = 1027000000.$
Answer$\text { Population of India in March } 2001=1027000000$
$=1.027000000 \times 10^9$
$=1.027 \times 10^9$
View full question & answer→Question 271 Mark
Write the numeral whose expanded form is given below:
$8 \times 10^5+6 \times 10^4+4 \times 10^3+2 \times 10^2+9 \times 10^1+6 \times 10^0$
Answer$8 \times 10^5+6 \times 10^4+4 \times 10^3+2 \times 10^2+9 \times 10^1+6 \times 10^0$
$=800000+60000+4000+200+90+6$
$=864296$
View full question & answer→Question 281 Mark
Express the following numbers in standard form: Distance between Earth and Moon $= 384000000m.$
AnswerDistance between Earth and Moon $=384000000 \mathrm{~m}$
$=3.84000000 \times 10^8$
$=3.84 \times 10^8$
View full question & answer→Question 291 Mark
Write $'T'$ for true and $'F'$ for false for the following: Reciprocal of $5^6$ is $6^5$.
AnswerFalse.
Reciprocal of $5^6$ = Reciprocal of $\Big(\frac{5}{1}\Big)^6=\Big(\frac{1}{5}\Big)^6$
View full question & answer→Question 301 Mark
Find the reciprocal of the following: $\Big(\frac{-5}{6}\Big)^{11}$
Answer$\Big(\frac{-5}{6}\Big)^{11}=\Big(\frac{-6}{5}\Big)^{11}$
View full question & answer→Question 311 Mark
Express the following numbers in standard form: The present age of universe $= 12000000000$ years.
AnswerThe present age of universe $=12000000000$ years
$=1.2000000000 \times 10^{10} \text { years }$
$=1.2 \times 10^{10} \text { years }$
View full question & answer→Question 321 Mark
Write the numeral whose expanded form is given below:
$9 \times 10^6+7 \times 10^5+0 \times 10^4+3 \times 10^3+4 \times 10^2+6 \times 10^1+2 \times 10^0$
Answer$9 \times 10^6+7 \times 10^5+0 \times 10^4+3 \times 10^3+4 \times 10^2+6 \times 10^1+2 \times 10^0$
$=9000000+700000+0+3000+400+60+2$
$=9703462$
View full question & answer→Question 331 Mark
Write the following numbers in expanded form:
$50074$
Answer$50074=5 \times 10^4+0 \times 10^3+0 \times 10^2+7 \times 10^1+4 \times 10^0$
View full question & answer→Question 341 Mark
Find the reciprocal of the following: $\Big(\frac{3}{8}\Big)^4$
Answer$\Big(\frac{3}{8}\Big)^4=\Big(\frac{8}{3}\Big)^4$
View full question & answer→Question 351 Mark
Find the value of the following: $6^\circ \times 7^\circ $
AnswerWe know that $\Big(\frac{\text{a}}{\text{b}}\Big)^\circ=1,$ therefore $6^\circ \times 7^\circ = 1 \times 1 = 1$
View full question & answer→Question 361 Mark
Express the following numbers in standard form:
Number of stars in a galaxy $= 100000000000.$
Answer$\text { Number of stars in a galaxy }=100000000000$
$=1.00000000000 \times 10^{11}$
$=1 \times 10^{11}$
View full question & answer→Question 371 Mark
Find the value of the following: $(-3)^\circ $
AnswerWe know that $\Big(\frac{\text{a}}{\text{b}}\Big)^\circ=1,$
therefore $(-3)^\circ = 1$
View full question & answer→Question 381 Mark
Express $2000000$ in standard form.
Answer$2000000=2.000000 \times 10^6$ [since the decimal point is moved $6$ places to the left]
$=2 \times 10^6$
View full question & answer→Question 391 Mark
Write $'T'$ for true and $'F'$ for false for the following:
$27000$ in standarf form is $27 \times 10^3$
AnswerFalse.
$27000=2.7 \times 10^4$ [Since the decimal point is moved 4 places to the left]
View full question & answer→Question 401 Mark
Write the reciprocal of:
$2^{5}$
AnswerWe know that the reciprocal of $\Big(\frac{\text{a}}{\text{b}}\Big)^\text{m}\text{ is }\Big(\frac{\text{b}}{\text{a}}\Big)^\text{m}$
Reciprocal of $2^5$ = Reciprocol of $\Big(\frac{2}{1}\Big)^5=\Big(\frac{1}{2}\Big)^5$
View full question & answer→Question 411 Mark
Write $'T'$ for true and $'F'$ for false for the following:
$654$ in standard form is $6.45 \times 10^2$
AnswerTrue.
$6.45 \times 10^2$ [Since the decimal point is moved $2$ places to the left]
View full question & answer→Question 421 Mark
Express the following as a rational number: $(-6)^{-1}$
Answer$(-6)^{-1}=\Big(\frac{1}{-6}\Big)^1$ $=\frac{1}{-6}=\frac{1\times(-1)}{-6\times(-1)}$ $=\frac{-1}{6}$
View full question & answer→Question 431 Mark
Express $6.4 \times 10^5$ in usual form.
Answer$6.4 \times 10^5=6.4 \times 100000$
$=640000$
View full question & answer→Question 441 Mark
Express the following as a rational number: $5^{-3}$
Answer$5^{-3}=\Big(\frac{1}{5}\Big)^{3}$ $=\frac{1}{5}\times\frac{1}{5}\times\frac{1}{5}$ $=\frac{1}{125}$
View full question & answer→Question 451 Mark
Write $'T'$ for true and $'F$' for false for the following: If $5-1\times \text{x}=8-1,$ then $\text{x}=\frac{8}{5}$
AnswerFalse.
$5^{-1}\times\text{x}=8^{-1}$
$\Rightarrow \frac{1}{5}\times \text{x}=\frac{1}{8}$
$\Rightarrow \text{x}=\Big(\frac{1}{8}\times5\Big)=\frac{5}{8}$
View full question & answer→Question 461 Mark
Find the reciprocal of the following:
$6^{7}$
Answer $6^{7}=\Big(\frac{1}{6}\Big)^7$
View full question & answer→Question 471 Mark
Express the following as a rational number:
$(4)^{-1}$
Answer $(4)^{-1}=\Big(\frac{1}{4}\Big)^1$
$=\frac{1}{4}$
View full question & answer→Question 481 Mark
Fill in the blank. If $9 \times 3^n=3^6$, then $n =$ .......... .
AnswerIf $9 \times 3^n=3^6$, then $n=\underline{4}$.
$\text { If } 9 \times 3^n=3^6$
$\Rightarrow 3^2 \times 3^n=3^6$
$\Rightarrow 3^{(2+n)}=3^6$
Equating the powers:
$\Rightarrow(2+n)=6$
$\Rightarrow n=(6-2)=4$
View full question & answer→Question 491 Mark
Express the following as a rational number: $\Big(\frac{-2}{3}\Big)^{-1}$
Answer$\Big(\frac{-2}{3}\Big)^{-1}=\Big(\frac{3}{-2}\Big)^1$ $=\frac{3}{-2}=\frac{3\times(-1)}{-2\times(-1)}$ $=\frac{-3}{2}$
View full question & answer→Question 501 Mark
Express the following as a rational number: $\Big(\frac{1}{3}\Big)^{-1}$
Answer$\Big(\frac{1}{3}\Big)^{-1}$ $=\Big(\frac{3}{1}\Big)^1=\frac{3}{1}$
View full question & answer→