Powers with like Bases

Q.

How do you simplify $8^{\frac{1}{3}}$?

Q. Find the value of ‘x’, when $3^x=\frac{\sqrt{3}}{9}$.

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

Q.

If $(2{)}^{m+1}\times 2^5=4^{-2}$ the value of $m$ is

___

Q. If $4^{{\sqrt{x}}^{\sqrt{x}}}=256$, the value of x is:

1. 4
2. $\sqrt{2}$
3. 2
4. 16

Q. Solve $9^{4x}÷3^{2x}=2187$ and find the value of x.

1. $x=\frac{-7}{6}$
2. $x=\frac{6}{7}$
3. $x=\frac{7}{6}$
4. $x=\frac{-6}{7}$

Q. Find the value of $m$ such that $5^{m+2}$ $\times$ $5^4$ = $5^3$.

Q.

If $a^{n+2}$ = $a^{2n-1}$, the value of n is :

1. 1

2. 2

3. 3

4. 0

Q. Verify that $(x÷$y)^{-1} = $x^{-1}÷y^{-1}$, if $x=\frac{-15}{26},y=\frac{5}{13}$

Q.

1. $5(p+4)$
2. $5(p-4)$
3. $(p-4)$
4. $(p+4)$

Q. Solve for $x$ in the equation $(-5{)}^{x+1}\times (-5{)}^5=(-5{)}^7$.

1. 6
2. 7
3. 2
4. 1

Q.

Evaluate $4^4\times 4^{-3}\times 4^2\times 4^{-5}$

1. $\frac{1}{4}$

2. 4

3. 16

4. $\frac{1}{16}$

Q.

If $m\ne n$ and $(m+n{)}^{-1}\times (m^{-1}+n^{-1})=m^x{n}^y$, then $x+y$ is equal to

1. -2

2. 1

3. 2

4. 0

Q. $\frac{2^5}{2^8}\times 2^{-7}$ =

1. $2^{10}$
2. $2^6$
3. $2^{-10}$
4. $2^{-4}$

Q. $(a+b)(a-b)(a^2+b^2$) is:

1. ($a^3-b^3$)
2. ($a^3+b^3$)
3. ($a^4+b^4$)
4. ($a^4-b^4$)

Q.

If, $x={\left(\frac{-4}{5}\right)}^{30}÷{\left(\frac{-4}{5}\right)}^{28}$ and $y={\left(\frac{-4}{5}\right)}^2\times {\left(\frac{-4}{5}\right)}^3$, find the value of $(x^3÷y{)}^2$

1. $\frac{-16}{25}$

2. $\frac{6}{25}$

3. $\frac{16}{25}$

4. $\frac{6}{16}$

Q. If $x={\left(\frac{-2}{5}\right)}^{30}÷{\left(\frac{5}{-2}\right)}^{-28}$ and $y={\left(\frac{-2}{5}\right)}^2\times {\left(\frac{-2}{5}\right)}^3$, then find the value of $(x^3÷y{)}^2$.

1. $\frac{-2}{5}$
2. $\frac{25}{4}$
3. $\frac{5}{40}$
4. $\frac{4}{25}$

Q.

Evaluate the exponential expression $x^5\times x^4$, for $x=2$

1. 32

2. 128

3. 256

4. 512

Q.

If $\frac{p}{q}={\left(\frac{2}{3}\right)}^2÷{\left(\frac{6}{7}\right)}^0$ then the value of ${\left(\frac{q}{p}\right)}^3$ is-

1. $\frac{28}{54}$

2. $\frac{54}{28}$

3. $\frac{729}{64}$

4. $\frac{64}{729}$

Q. Find the value of 'n' in each of the following :
i) ${\left(\frac{2}{3}\right)}^3\times {\left(\frac{2}{3}\right)}^5={\left(\frac{2}{3}\right)}^{n-2}$
ii) $(-3{)}^{n+1}\times (-3{)}^5=(-3{)}^{-4}$
iii) $7^{2n+1}÷49=7^3$

Q. ${\left(\frac{1}{4}\right)}^{-2}÷{\left(\frac{1}{4}\right)}^{-3}=$

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

Q. If $x={\left(\frac{-2}{5}\right)}^{30}÷{\left(\frac{5}{-2}\right)}^{-28}$ and $y={\left(\frac{-2}{5}\right)}^2\times {\left(\frac{-2}{5}\right)}^3$, then find the value of $(x^3÷y{)}^2$.

1. $\frac{5}{40}$
2. $\frac{-2}{5}$
3. $\frac{4}{25}$
4. $\frac{25}{4}$

Q.

If $m$ and $n$ are integers, $a$ is a non-zero integer and $a^m$ × $a^n$ =$a^x$, then the value of $x$ is _____.

1. $mn$
2. $m+n$
3. $m-n$
4. $\frac{m}{n}$

Q. If $x={\left(\frac{-2}{5}\right)}^{30}÷{\left(\frac{-2}{5}\right)}^{28}$ and $y={\left(\frac{-2}{5}\right)}^2\times {\left(\frac{-2}{5}\right)}^3$, then find the value of $(x^3÷y{)}^2.$

1. $\frac{5}{40}$
2. $\frac{-2}{5}$
3. $\frac{4}{25}$
4. $\frac{25}{4}$

Q. Simplify:
$[{\left(\frac{1}{2}\right)}^{-3}+{\left(\frac{1}{3}\right)}^{-3}+{\left(\frac{1}{4}\right)}^{-3}]÷{\left(3\right)}^2$

Q. Evaluate
$\frac{(-1{)}^{13}}{2^3}+\frac{2^3-1^{10}+3^2}{3^2-2^2}+{\left(\frac{7}{11}\right)}^3÷\frac{98}{121}$

1. $3\frac{17}{44}$
2. $3\frac{173}{440}$
3. $3\frac{137}{440}$
4. $3\frac{21}{440}$

Q. ${\left(\frac{1}{2}\right)}^{-2}÷{\left(\frac{1}{2}\right)}^{-3}=$

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

Q.

${\left(-3\right)}^2\times {\left(-3\right)}^5=\_\_\_\_\_\_\_({\left(-3\right)}^{2\times 5}/{\left(-3\right)}^{2+5})$

Q.

Simplify and write in exponential form: $4^3\times 4^{-2}\times {16}^2$

1. 4³

2. 4⁴

3. 4⁵

4. 4⁶

Q. If $5^{m+2}$ $\times$ $5^4$ = $5^3$ , then $m$ = .

1. \N
2. -1
3. -4
4. -3

Q.

Simplify ${(2^5÷2^8)}^5$ × $2^{-5}.$

1. $\frac{1}{2^{10}}$

2. $\frac{1}{2^{20}}$

3. $\frac{1}{2^{(-15)}}$

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