Multiplying Powers with the Same Exponents

Q. The value of $(27\times 125{)}^{\frac{1}{3}}$ is __.

1. $35$
2. $15$
3. $25$
4. $51$

Q. Find the value of $(3^{-2}{)}^2$.

1. $\frac{1}{18}$
2. $\frac{1}{81}$
3. 81
4. -81

Q.

Find the value of 'n' if ${\left(a^m\right)}^{2n}=a^{2m}$ [4 MARKS]

Q. If $x=y^a,y=z^b,z=x^c$ then find abc. [4 MARKS]

Q.

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

1. -4

2. -6

3. -8

4. -10

Q. Using laws of exponents, simplify and write the answer in exponential form:
$6^{15}÷6^{10}$

Q.

Fill in the blanks with $<,>$ or $=$ sign: $3^2$ _____ $15$

Q.

Express the following products as powers. Indicate the base and index in each case.

$a\times a\times a$

Q. Simplify the following using law of exponents.
$\left[\right(\frac{-5}{6}{)}^2{]}^5$

Q.

$({10}^2{)}^2$ = __.

Q. The value of $3^0+4^0-5^0$ is .

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

Q.

If a = 2 and b = 3. Find the value of $a^b\times b^a$.

1. 56

2. 72

3. 64

4. 8

Q.

Verify that :

${(-4)}^8÷{(-4)}^5={(-4)}^3$.

Q. ${\left(2\right)}^5\times {\left(4\right)}^5={\left(24\right)}^5$.

1. True
2. False

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

Q. Using laws of exponents, simplify and write the answer in exponential form:
$2^5\times 5^5$

Q.

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

___

Q.

$a^m\times b^m=(ab{)}^m$

1. False

2. True

Q.

If $a^m$ × $a^n$ = $a^x$, then the value of $x$ is _____. (where m and n are natural numbers)

1. $mn$

2. $m+n$

3. $m-n$

4. $\frac{m}{n}$

Q. $2^5\times 3^4$ =

1. 2674
2. 2592
3. 2400
4. 2544

Q.

Evaluate the exponential expression $x^5$ × $x^4$, for$x=2$.

1. $32$

2. $128$

3. $256$

4. $512$