Power of a Power

Q. FIND THE SQUARE ROOT OF 7-4\sqrt3

Q.

Simplify :$2^{\frac{2}{3}}\times 2^{\frac{1}{5}}$

Q. Find the value of $2^{-4}$

Q.

Question 4(i)
Evaluate:

$\frac{8^{-1}\times 5^3}{2^{-4}}$

Q.

Find $x$, if $9\times 3^x=(27{)}^{2x-3}$

Q.

By what number should ${\left(\frac{1}{2}\right)}^{-1}$ multiplied so that the product may equal to ${\left(\frac{-4}{7}\right)}^{-1}?$

Q.

Evaluate ${\left(102\right)}^3$ ($3$ is power) using suitable identities

Q. ${\left[\frac{(169{)}^{-3}}{(196{)}^{-8}}\right]}^{\frac{1}{48}}$ is equal to _____.

Q. Express ${16}^{-2}$ as a power with the base 2.

1. $2^8$
2. $2^{16}$
3. $2^{-16}$
4. $2^{-8}$

Q.

If $\frac{(a^n+b^n)}{(a^{n-1}+b^{n-1})}$ is the G.M of $a$ and $b$ then $n=(a,b\in R+,a\ne b)$

1. $0$

2. $1$

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

4. $-2$

Q.

Find the value of ${\left(\frac{2}{5}\right)}^{-2}$

1. 

2. 

3. 

4. 

Q.

Simplify :

$\left(i\right)8^{\frac{4}{3}}+{25}^{\frac{3}{2}}-{\left(\frac{1}{27}\right)}^{-\frac{2}{3}}\left(ii\right)\left[\right(64{)}^{-2}{]}^{-3}÷\left[\right\{(-8{)}^2{\}}^3{]}^2(iii\left)\right(2^{-3}-2^{-4}\left)\right(2^{-3}+2^{-4})$

Q.

If $16\times 8^{n+2}=2^m$, find the value of $m$

Q.

Simplify: ${\left({64}^{\frac{2}{3}}\times 2^{-2}\times 8^0\right)}^{\frac{1}{2}}$

Q.

Find $x$, if $4^{2x}=\frac{1}{32}$.

1. $\frac{5}{4}$

2. $\frac{-5}{4}$

3. $\frac{-4}{5}$

4. $\frac{4}{5}$

Q. Solve for y if
$\frac{{\left(\frac{1}{9}\right)}^{2y-1}(.0081{)}^{\frac{1}{3}}}{\sqrt{243}}={\left(\frac{1}{3}\right)}^{2y-5}\sqrt[3]{3\frac{{27}^{y-1}}{10000}}$

1. $19\times 8$
2. $\frac{-19}{8}$
3. $\frac{18}{9}$
4. $\frac{-19}{18}$

Q. $(9{)}^2$ as a power with base 3 is .

1. $3^4$
2. $3^3$
3. $3^5$
4. $3^2$

Q.

Simplify the following mathematical expression:

$18+10-7\times 32÷\frac{1}{3}$of $24$

Q.

Question 85 (b)

Evaluate
$\frac{5^4\times 7^4\times 2^7}{8\times 49\times 5^3}$

Q.

The value of $\sqrt[3]{3343}\times \sqrt[3]{364}$ is

1. 28

2. - 28

3. 18

4. - 18

Q.

$a^{\left(\frac{m}{n}\right)}$ can be written as:

1. $\sqrt[m]{m\left(a^n\right)}$

2. $\sqrt[n]{n\frac{1}{\left(a^m\right)}}$

3. $\sqrt[n]{n\left(a^m\right)}$

4. $\sqrt[n]{n\frac{1}{\left(a^m\right)}}$

Q.

Find the value of x:
${(15\times 0.40)}^4÷{(1080÷30)}^4\times {(27\times 8)}^4={(3\times 2)}^{x+5}$

1. 4

2. 5

3. None of these

4. 3

Q.

Express each o fthe following rational numbers with a negative exponent:

$\left(i\right){\left(\frac{1}{4}\right)}^3\left(ii\right)3^5\left(iii\right){\left(\frac{3}{5}\right)}^4\left(iv\right){\left\{{\left(\frac{3}{2}\right)}^4\right\}}^{-3}\left(iv\right){\left\{{\left(\frac{7}{3}\right)}^4\right\}}^{-3}$

Q.

Evaluate : $\frac{x^{5+n}(x^2{)}^{3n+1}}{x^{7n-2}}$

Q.

Solve: $2^{x+1}=8^x$

1. 3

2. 1

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

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

Q.

Prove that :

$\left(i\right){\left(\frac{x^a}{x^b}\right)}^{\frac{1}{ab}}{\left(\frac{x^b}{x^c}\right)}^{\frac{1}{bc}}{\left(\frac{x^c}{x^a}\right)}^{\frac{1}{ca}}=1\left(ii\right)\frac{1}{1+x^{a-b}}+\frac{1}{1+x^{b-a}}=1$

Q.

Evaluate : ${27}^{\frac{2}{3}}+(\frac{81}{16}{)}^{\frac{-1}{4}}$

1. $9\frac{2}{3}$

2. $10\frac{2}{3}$

3. $10$

4. $\frac{29}{3}$

Q.

Exponent of the final value of {($3^{-5}$) × (${10}^{-5}$) × 125} / {($5^{-7}$) × ($6^{-5}$)} is 5.

1. False

2. True

Q.

If ${\left(2000\right)}^{10}=1.024\times {10}^k$, then the value of $k$ is

1. $33$

2. $30$

3. $34$

4. $31$

Q.

For a non-zero rational number a, $(a^3{)}^{-2}$ is equal to

1. $a^6$

2. $a^{-6}$

3. $a^1$

4. $a^{-9}$