Division of Powers with the Same Base

Q. Simplify $\frac{(-2{)}^3\times (-2{)}^7}{3\times 4^6}.$

1. $\frac{1}{6}$
2. $\frac{1}{12}$
3. $\frac{2}{3}$
4. 2

Q. The value of $\frac{{10}^{22}+{10}^{20}}{{10}^{20}}$ is ___.

1. ${10}^2$
2. $101$
3. $10$
4. ${10}^0$

Q.

Find the value of $(\frac{-2}{5}{)}^7÷(\frac{-2}{5}{)}^6$.

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

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

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

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

Q. By what number should 4^4 be divided with to get 4?​

1. 4
2. 4^3
3. 4^2
4. 4^4

Q. Find the value of 5⁴ ÷ 5³.

1. 5
2. 125
3. 625
4. 25

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.

Solve:-

$(\frac{2^5}{2^8})\times 2^{-7}$

1. $2^{10}$

2. $2^6$

3. $2^{-10}$

4. $2^{-4}$

Q. Match the values with the corresponding laws of exponents.

1. $2^4\times 3^4=6^4$
2. $\frac{4^7}{4^5}=4^2$
3. $3^7\times 3^2=3^9$
4. $(2^7{)}^4=2^{28}$

Q.

The value of ${\frac{(-7)}{\left(7^6\right)}}^6$ is:

__

Q. Find the value of ${100}^{\frac{5}{2}}÷{100}^{-\frac{1}{2}}$.

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

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

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

Q. The value of $\frac{(-7{)}^6}{7^6}$ is .

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