Exponent of a Product

Q. $\left[\right(\frac{1}{2}{)}^{-1}+(\frac{2}{3}{)}^2-(\frac{3}{4}{)}^0{]}^{-2}$ is equal to

1. $\frac{169}{81}$
2. $\frac{81}{169}$
3. $\frac{-81}{169}$
4. $\frac{81}{169}$

Q. Evaluate: $(4^{-1}+8^{-1})÷(\frac{2}{3}{)}^{-1}$

1. $\frac{1}{4}$
2. $\frac{1}{-4}$
3. 4
4. -4

Q.

Find the value of ${\left(\frac{16}{81}\right)}^{-3/4}÷{\left(\frac{243}{32}\right)}^{3/5}$ of ${\left(\frac{9}{4}\right)}^{-1/2}$

Q. The value of $(27\times 125{)}^{\frac{1}{3}}$ is __.

Q. Evaluate :
iv) $(0.4{)}^3$

Q. Match the following

1. $(\frac{a}{b}{)}^m$
2. 1
3. $a^{mn}$
4. $(ab{)}^m$

Q. Evaluate $2^2\times 5^2$

1. $7^4$
2. 49
3. 100
4. 1000

Q. If $a\ne 0$ and $m=n$, then $\frac{a^m}{a^n}$ = .

1. 1
2. $a^{2m}$
3. \N

Q. Simplify $(-2{)}^{-5}\times (3{)}^{-5}\times (4{)}^{-5}$.

1. $\frac{1}{(24{)}^5}$
   
2. $\frac{1}{(-24{)}^5}$
3. $(-25{)}^5$
4. $5^{-5}$

Q. Simplify and express the answer in the positive exponenet form:
(i) $\frac{(-3{)}^3\times 2^6}{6\times 2^3}$
(ii) $\frac{(2^3{)}^5\times 5^4}{4^3\times 5^2}$

Q. State True or False
The value of $(27\times 125{)}^{\frac{1}{3}}$ is 15.

Q. Find the value of $(5^5\times 3^5)+(5^0\times 3^0)$.

1. ${15}^5+2$
2. ${15}^5+1$
3. ${15}^5$
4. None of these

Q. Evaluate: $[{\left(\frac{5}{6}\right)}^2\times \frac{9}{4}]÷[(-\frac{3^2}{2})\times \frac{125}{216}]$

Q. Find the value of 'm', if $4^6\times 5^6={20}^m$

1. 12
2. 1
3. 6
4. 36

Q.

Find the value of $3^4\times 2^4$.

1. 216

2. 1200

3. 1286

4. 1296

Q. Simplify : $\frac{{\left(\frac{1}{x}\right)}^{-1}}{{\left(\frac{1}{x}\right)}^3}$

Q. Simplify the following using law of exponents.
$(-3{)}^3\times (-5{)}^3$ = $m^3$. Find m

Q. If $3^2\times x=81$, Find $x$.

Q. $2^m\times 3^m$ is equal to

1. $(6{)}^m$
2. $(6{)}^{2m}$
3. $(2\times 3{)}^m$
4. $(2\times 3{)}^{2m}$

Q. Simplify $(\frac{3}{8}{)}^4\times (\frac{7}{5}{)}^4$

1. $(\frac{21}{45}{)}^4$
2. $(\frac{10}{13}{)}^4$
3. $(\frac{21}{40}{)}^4$
4. $(\frac{21}{48}{)}^4$

Q. Find the value of $(5{)}^6\times (7{)}^6$.

1. $(30{)}^6$
2. $(35{)}^5$
3. $(35{)}^6$
4. $(40{)}^6$

Q. $2^5\times 4^5$ can be expressed as _____.

1. $8^{-5}$
2. $8^{-4}$
3. $8^4$
4. $8^5$

Q. The value of $(27\times 125{)}^{\frac{1}{3}}$ is __.

1. $35$
2. $25$
3. $15$
4. $51$

Q. The value of $(27\times 125{)}^{\frac{1}{3}}$ is __.

1. $35$
2. $25$
3. $15$
4. $51$

Q. Product of all the even divisors of $N=1000$, is

1. $32\cdot {10}^2$
2. $64\cdot 2^{14}$
3. $64\cdot {10}^{18}$
4. $128\cdot {10}^6$

Q.

Simplify :

(vii) ${(-3)}^2\times {(-5)}^2$

Q. Which of the following option is equal to $125x^3\times 6^3{y}^3?$

1. $(6xy{)}^3$
2. $(5xy{)}^3$
3. $(30xy{)}^3$
4. All of the above.

Q. Show that ${2.7}^n+{3.5}^n-5$ is a multiple of $24$.

Q. Find the value of ${(-2)}^3$ × ${(-3)}^2$.

1. $(-72)$
2. $27$
3. $(-27)$
4. $72$