Laws of Exponents for Real Numbers

Q.

$\text{If}{\left(\sqrt{1024}\right)}^3=8^x\text{, then}x\text{is}$ ________.

1. 15

2. 10

3. 2

4. 5

Q. If $2^a=3^b=6^c$ then

1. $c=\frac{a+b}{a-b}$
2. $c=\frac{a{b}^2}{a^2+b^2}$
3. $c=\frac{ab}{a+b}$
4. $c=\frac{a{b}^2}{a^2-b^2}$

Q. When expanded, the number of zeroes in ${1000}^{10}$ is ______.

1. 13
2. 30
3. 4
4. 10

Q.

Simplify ${\left(256\right)}^{\frac{-1}{2}}$.

1. 16

2. 4

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

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

Q.

Simplify $\frac{{27}^{\frac{2}{3}}}{9^{\frac{1}{2}}{3}^{\frac{3}{2}}}$

1. $\sqrt{3}$

2. $1÷\sqrt{3}$

3. $3\sqrt{3}$

4. $1÷3\sqrt{3}$

Q.

If ${\left[{\left\{{\left(\frac{1}{7^2}\right)}^{-2}\right\}}^{-\frac{1}{3}}\right]}^{\frac{1}{4}}=7^m$ then find the value of m.

1. $\frac{2}{8}$

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

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

4. $-\frac{1}{7}$

Q. The value of $\frac{(0.6{)}^0-(0.1{)}^{-1}}{\left(\frac{3}{2^3}{)}^{-1}\right(\frac{3}{2}{)}^3+(-\frac{1}{3}{)}^{-1}}$ is _____________.

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

Q.

What is the value of the expression $\frac{a^m}{a^n}$?

1. $a^{mn}$

2. $a^{\frac{m}{n}}$

3. $a^{m+n}$

4. $a^{m-n}$

Q. Simplify:${64}^{\frac{1}{3}}[{64}^{\frac{1}{3}}-{64}^{\frac{2}{3}}]$

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

Q. Simplify:
(i) $\frac{{11}^{\frac{1}{2}}}{{11}^{\frac{1}{4}}}$ (ii) $7^{\frac{1}{2}}{.8}^{\frac{1}{2}}$
[2 Marks]
[RS Aggarwal]
[Operations on Real Numbers]