Free Printable Power Rule of Exponents

1.

According to exponent rules, when we raise a power to a power we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

2.

Simplify the following expression:

(x⁵)⁴

a)

x⁹

b)

x²⁰

c)

x

d)

x⁵⁴

3.

Simplify the following expression:

(b³)⁸

a)

b¹¹

b)

8b³

c)

b²⁴

d)

24b

4.

Simplify the following expression:

(3y⁴)²

a)

9y⁸

b)

9y⁶

c)

6y⁸

d)

6y⁶

5.

(2ab)³

a)

2³a³b³

b)

2ab³

c)

6a³b³

d)

6ab

6.

Simplify the following expression:

(3x³y⁵)⁴

a)

3x¹²y²⁰

b)

81x¹²y²⁰

c)

12x¹²y²⁰

d)

81x⁷y⁹

7.

Which shows the Power Rule used correctly? $\left(ab\right)^5$

a)

$ab^5$

b)

$a^5b^5$

c)

$a^5b$

d)

$a^6b^6$

8.

Simplify. $\left(m^3\right)^5$

a)

$m^8$

b)

$m^{15}$

c)

$8m$

d)

$15m$

9.

Simplify. $\left(5y^3z^2\right)^5$

a)

$5^5y^{15}z^{10}$

b)

$5^5y^8z^7$

10.

Simplify. $\left(2cd^2\right)^4$

a)

$2^4c^4d^6$

b)

$2^4c^4d^8$

11.

$\left(x^5y^7\right)^3\ =\ x^{15}y^{21}$

a)

True

b)

False

12.

Simplify the following expression:

(2x³y)⁶

**HINT: Distribute the exponent to all terms inside the parenthesis**

a)

2x¹⁸y⁶

b)

64x¹⁸y⁶

c)

64x³y⁶

d)

2x³y⁶

13.

If (2^x)⁵=2¹⁵, what does x equal?

a)

x = 3

b)

x = 5

c)

x = 10

14.

(5²c³)⁵

a)

10⁵c⁵

b)

5⁷c⁸

c)

5¹⁰c¹⁵

d)

5¹⁰/c¹⁵

15.

Which of the following expressions is equivalent to (2x)³ ?

a)

(2x)(2x)(2x)

b)

2(x)(x)(x)

c)

2x + 2x + 2x

d)

2x⋅3

16.

Simplify the expression

$\left(3^2\right)^3$

a)

$3^6$

b)

$3^9$

c)

$3^5$

17.

Simplify the expression

$\left(\left(9.2\right)^3\right)^7$

a)

$9.2^{10}$

b)

$9.2^{21}$

18.

Simplify the expression

$\left(\left(-2w\right)^2\right)^3$

a)

$64w^6$

b)

$64w^5$

c)

$-64w^6$

d)

$-64w^5$

Power Rule of Exponents

Total questions: 18

Worksheet time: 5hrs 30mins

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