Division of Exponents Having the Same Base

Q. By what number should $3^{-4}$ be multiplied so that the product is 729?

1. $3^{10}$
2. $3^{11}$
3. $3^{12}$
4. $3^{13}$

Q.

Find the product: $\left(-\frac{10}{3}p{q}^3\right)\times \left(\frac{6}{5}{p}^{3}q\right)$

Q. By what number should $2^{-5}$ be multiplied so that the product is 1024?

1. $2^{16}$
2. $2^{15}$
3. $2^{17}$
4. $2^{13}$

Q.

If $x$ be any non-zero integer, then $x^{-1}$ is equal to:

1. $x$

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

3. $-x$

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

Q.

Find the number from each of the following expanded forms: ${(4\times 10)}^5+{(5\times 10)}^3+{(3\times 10)}^2+{(2\times 10)}^0$.

Q. Evalute:
$(3^0{)}^6$

Q. Simplify $\frac{{18}^{15}}{{18}^5}$

1. ${18}^{20}$
2. ${18}^{10}$
3. ${18}^{15}$
4. 18

Q. Find the value of x, if $\frac{8^x}{8^9}=8^{15}$.

1. 25
2. 24
3. 20
4. 23

Q. Find the value of 'n' if $\frac{(9{)}^{18}}{(9{)}^n}=9^{11}$

1. 9
2. 6
3. 7
4. 5

Q.

$15y^8÷5y^6$ is $3y^2$

1. False

2. True

Q. The value of $\frac{7^5}{7^2}$ is _____ .

1. $7^5$
2. $7^3$
3. $7^4$
4. $7^2$

Q.

If ${17}^{\frac{1}{5}x}=289$, find the value of $x$

Q. Mr Gupta asked two of his students to solve the expression ${\left(\frac{9a^3{b}^{-8}}{81a^{-5}{b}^2}\right)}^{-\frac{1}{2}}$ and write the answer on the blackboard. Aryan wrote the answer as $3a^{-4}{b}^5$, whereas Ayan wrote the answer as $\frac{3b^5}{a^4}$. Who wrote the correct answer?

1. Both of them
2. Ayan
3. Aryan
4. None of these

Q. Find the value of $(2^3\times 5^3\times 7^0)$.

1. 1000
2. 100
3. 700
4. 343

Q.

If $3^x=5^y={75}^z$ show that $z=\frac{xy}{2x+y}$

Q.

Simplify the expression. Write your answer as a power.
$\frac{5^2\times 5^9}{5}$

Q.

Simplify the expression . Write your answer as a power.

${\left({\mathrm{n}}^{11}\right)}^2$

Q. $\frac{\left(a^m\right)\times \left(a^n\right)}{\left(a^p\right)}$ can be rewritten as:

1. $a^{p-m+n}$
2. $a^{m+n-p}$
3. $a^{mnp}$
4. $a^{p-mn}$

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

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

Q. By what number should $5^2$ be multiplied so that the product is 3125 .

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

Q. Use the law of exponents and simplify:
$\frac{2^{3^2}}{{\left(2^3\right)}^2}$

Q. Simplify $\frac{4^{3}x{a}^9{b}^6{c}^2}{4^{2}x{a}^4{b}^{5}c}$.

1. 4$a^{5}c$
2. 4$a^{5}bc$
   
3. 4$a^5{b}^{2}c$
4. 4$xabc$

Q.

Using laws of exponents , simplify : $\frac{{\left(2x^2\right)}^3}{{\left(5x\right)}^{-2}}$

Q. $\frac{5^{10+n}\times {25}^{3n-4}}{5^{7n}}$ = ___

Q. Using laws of exponents, simplify and write the answer in exponential form:
${\left(5^2\right)}^2÷5^3$

Q. Which of the following are true

1. $\frac{a^m}{a^n}=a^{m-n}$, if m>n
2. $\frac{a^m}{a^n}=a^{m-n}$, if n>m
3. $\frac{a^m}{a^n}=\frac{1}{a^{n-m}}$, if n>m
4. $\frac{a^m}{a^n}=\frac{1}{a^{n-m}}$, if m>n

Q. Find the value of $\frac{100}{10000}$.

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

Q. $\frac{3^5}{3^2}=3^3$

1. True
2. False

Q. Find the value of $2^{-5}\times 2^4$.

1. $2^9$
2. $2^{-1}$
3. $2^{-20}$
4. $2^{-3}$

Q. Divide, Write the quotient and the remainder.
$40m^2÷30m^3$