Free Printable Product of Powers VS Power of Powers (Exponents)

1.

(r⁴)⁶

a)

10r

b)

r¹⁰

c)

24r

d)

r²⁴

2.

(x⁵)⁴

a)

x⁹

b)

x²⁰

c)

x

d)

x⁵⁴

3.

Simplify:

$10^5\cdot10^7$

a)

$10^{35}$

b)

$100^{12}$

c)

$10^{12}$

d)

None of the above

4.

(ab)²

a)

ab²

b)

a²b²

c)

a²b

5.

Simplify: (4x⁵)²

a)

16x¹⁰

b)

8x¹⁰

c)

16x⁷

d)

8x⁷

6.

Simplify:

$t^9\cdot t^8$

a)

$t^1$

b)

$t^{72}$

c)

$t^{17}$

d)

None of the above

7.

Simplify:

$y^{12\ }\cdot y^{10}$

a)

$y^2$

b)

$y^{22}$

c)

$y^{120}$

d)

None of the above

8.

Simplify:

$7^8\cdot7$

a)

$7^9$

b)

$49^8$

c)

$7^8$

d)

None of the above

9.

Simplify:

$\left(6x^2\right)\left(-3x^5\right)$

a)

$18x^7$

b)

$-18x^7$

c)

$3x^7$

d)

None of the above

10.

Simplify:

$c^5\cdot c^3\cdot c^3$

a)

$c^{45}$

b)

$3c^{11}$

c)

$c^{11}$

d)

None of the above

11.

Simplify:

$2m^4\cdot5m^2$

a)

$10m^6$

b)

$10m^8$

c)

$7m^6$

d)

None of the above

12.

Simplify:

$x^3\cdot x^5\cdot x^{10}$

a)

$x^2$

b)

$18x$

c)

$x^{150}$

d)

None of the above

13.

Simplify:

$3x^2\left(-5x^4\right)$

a)

$15x^2$

b)

$-15x^8$

c)

$-2x^6$

d)

None of the above

14.

Simplify:

$10u^3v^5\cdot7v^3$

a)

$70u^3v^{15}$

b)

$17u^3v^8$

c)

$70u^3v^8$

d)

None of the above

15.

Simplify:

$2m^4\cdot5m^2$

a)

$10m^6$

b)

$10m^8$

c)

$7m^6$

d)

None of the above

16.

Find the missing exponent:

$3^{16}=3^8\cdot3^?$

a)

2

b)

8

c)

4

d)

1

17.

Billy was asked to solve 3⁵∙3⁴. He got 9²⁰. What error did he make?

a)

When he multiplies exponents, he is supposed to add the base and the exponent

b)

When he multiplies exponents, he is supposed to multiply the base and keep the exponents

c)

When he multiplies exponents, he is supposed to keep the base and add the exponents if the base is the same

d)

None of the above

18.

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

a)

add

b)

subtract

c)

multiply

d)

divide

19.

According to exponent rules, when we simplify (x²)⁵ we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

20.

Simplify (wm⁵)³

a)

w³m¹⁵

b)

wm¹⁵

c)

w⁴m⁸

d)

w³m⁸

21.

Simplify (wx⁴z²)⁵

a)

wx²⁰z¹⁰

b)

w⁵x²⁰z¹⁰

c)

w⁶x⁹z⁷

d)

wx⁹z⁷

22.

X^m•Xⁿ

a)

X^MN

b)

X^M+N

c)

X^m+n

23.

Identify the correct expanded form and value for the power.

\left(-1\right)^5

a)

$\left(-1\right)\left(-1\right)\left(-1\right)\left(-1\right)\left(-1\right)\ =\ 1$

b)

$\left(-1\right)\left(-1\right)\left(-1\right)\left(-1\right)\left(-1\right)=-1$

c)

$\left(5\right)\left(-1\right)\ =-5$

d)

$\left(-1\right)\left(5\right)=-5$

24.

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

25.

Which option follows the product of a power rule for exponents with the same base?

a)

(9²)(9¹) = 9³

b)

(9²)(9¹) = 9¹

c)

(9²)(9¹) = 9²

26.

Which option follows the product of a power rule for exponents with the same base?

a)

(e⁴)(e¹) = e⁴

b)

(e⁴)(e¹) = e³

c)

(e⁴)(e¹) = e⁵

27.

Which option follows the product of a power rule for exponents with the same base?

a)

(7⁹)(7⁹) = 7¹⁸

b)

(7⁹)(7⁹) = 7⁸¹

c)

(7⁹)(7⁹) = 7⁰

28.

Which option follows the product of a power rule for exponents with the same base?

a)

(m¹)(m³) = m²

b)

(m¹)(m³) = m⁴

c)

(m¹)(m³) = m³

29.

Which option follows the product of a power rule for exponents with the same base?

a)

(2⁹)(2²) = 2⁷

b)

(2⁹)(2²) = 2¹⁸

c)

(2⁹)(2²) = 2¹¹

30.

Simplify (2x⁴y⁷)³

a)

6x⁷y¹⁰

b)

6xy³²

c)

8x¹²y²¹

31.

If (2^x)⁵=2¹⁵, what does x equal?

a)

x = 3

b)

x = 5

c)

x = 10

32.

Simplify (-1/2)⁰

a)

1

b)

0

c)

-1

d)

-2

Product of Powers VS Power of Powers (Exponents)

Total questions: 32

Worksheet time: 32mins

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