Free Printable Power and Product Rule

1.

Simplify:

$7a^2\cdot\left(5a^6b\right)^2$

a)

^{$35a^{14}b^2$}

b)

$175a^{12}b^2$

c)

^{$175a^{14}b^2$}

d)

$35a^{14}b$

2.

Simplify:

$2x^2y^3\cdot\left(-4xy\right)^2$

a)

$16x^3y^6$

b)

$-32x^4y^5$

c)

$-8x^4y^6$

d)

$32x^4y^5$

3.

What is the area of the rectangle with the given sides?

a)

$7x^3y^8z^4$

b)

$10x^2y^{16}z^3$

c)

$10x^3y^8z^4$

d)

None of the above

4.

Simplify:

$-3xy^3\cdot\left(4xy\right)^2$

a)

$-12x^3y^5$

b)

$-48x^2y^4$

c)

$-48x^3y^5$

d)

$-12x^2y^6$

5.

Find the area of the triangle given:
B = $3b^2$
H = $12p^7b^{19}$

Hint: $A=\frac{1}{2}Bh$

a)

$18b^{21}p^7$

b)

$18b^7p^{21}$

c)

$36b^{21}p^7$

d)

$36b^{38}p^7$

6.

Simplify:

$\left(3x^4y^5\right)^2\cdot\left(-2x^2y^{-1}\right)^3$

a)

$-72x^{14}y^7$

b)

$72x^{14}y^{13}$

c)

$-72x^2y^{13}$

d)

$-6x^{14}y^7$

7.

Simplify:

$\left(x^2\right)^3\cdot3x^3$

a)

$3x^8$

b)

$3x^{18}$

c)

$9x^9$

d)

$3x^9$

8.

Simplify:

$\left(m^3n^4\right)^4\cdot\left(mn^3\right)^2$

a)

^{$m^{14}n^{22}$}

b)

^{$m^{13}n^{22}$}

c)

^{$m^9n^{13}$}

d)

None of the above

9.

Simplify:

$\left(y^3\right)^3\cdot yx^4\cdot x^2$

a)

$x^6y^7$

b)

$x^6y^{10}$

c)

$x^8y^{10}$

d)

None of the above

10.

Simplify:

$\left(y^3\right)^3\cdot\left(2x^4\right)^4$

a)

$8x^{16}y^9$

b)

$16x^8y^6$

c)

$2x^{16}y^9$

d)

$16x^{16}y^9$

11.

Simplify:

$a^4b^3\cdot\left(2a^2\right)^4$

a)

$8a^{12}b^3$

b)

$16a^{12}b^3$

c)

$2a^{12}b^3$

d)

None of the above

12.

Simplify:

$\left(2x^2\cdot2x^4y^3\right)^4$

a)

$16x^{10}y^7$

b)

$32x^{24}y^{12}$

c)

$256x^{24}y^{12}$

d)

None of the above

13.

Find the missing exponent:

$5y^2\cdot\left(2y^3\right)^?=80y^{14}$

a)

9

b)

4

c)

3

d)

2

14.

Simplify:

$\left(2x^{-3}\right)^2\left(x^5y\right)^2$

a)

$4x^4y^2$

b)

$4x^2y^2$

c)

$4y^2$

d)

None of the above

15.

Simplify:

$\left(-5a^{-3}\right)\left(3a^6b\right)^2$

a)

$-15a^9b$

b)

$45a^9b$

c)

$-45a^9b^2$

d)

None of the above

16.

Simplify.

(5cd⁴) (2c³d²)

a)

10c⁴d⁶

b)

7c⁴d⁶

c)

7c³d⁸

d)

10c³d⁸

17.

Simplify.

(4st) (-3s³) (t⁵)

a)

-12s⁴t⁶

b)

12s⁶t⁸

c)

-7s⁴t⁶

d)

-12s⁶t⁸

18.

Simplify.

(-7x³y²)²

a)

49x⁶y⁴

b)

-14x⁶y⁴

c)

-14x⁵y⁴

d)

-49x⁶y⁴

19.

Simplify.

(-2mn) (3m²n⁴)²

a)

-18m⁵n⁹

b)

-12m⁵n⁹

c)

-18m⁵n⁷

d)

-12m⁵n⁷

20.

Simplify.

3(-2x³y⁴)⁴

a)

48x¹²y¹⁶

b)

-48x¹²y¹⁶

c)

-24x¹²y¹⁶

d)

-24x⁷y⁸

21.

(r⁴)⁶

a)

10r

b)

r¹⁰

c)

24r

d)

r²⁴

22.

(3⁴)(3⁷)

a)

3²⁸

b)

3³

c)

3^-3

d)

3¹¹

23.

(8⁵)³

a)

8⁸

b)

8¹⁵

c)

8²

d)

1/8²

24.

Power Rule states: keep the base the same and do this to the exponents.

a)

multiply

b)

add

c)

subtract

d)

divide

25.

Product Rule states: keep the base the same and do this to the exponents.

a)

multiply

b)

add

c)

subtract

d)

divide

26.

Simplify
(3x³y⁵)⁴

a)

3x¹²y²⁰

b)

81x¹²y²⁰

c)

12x¹²y²⁰

d)

81x⁷y⁹

27.

(4x⁵y²)(6x²y³)

a)

10x¹⁰y⁶

b)

24x⁷y⁵

c)

24x¹⁰y⁶

d)

10x⁷y⁵

28.

Simplify: (-3x⁴)(5x²)

a)

-15x⁸

b)

-15x⁶

c)

2x⁸

d)

2x⁶

29.

What is the BASE in the exponent below?
4³

a)

4

b)

3

c)

4³

d)

64

30.

4⁵ x 4

a)

4⁵

b)

4

c)

4⁶

d)

4⁴

31.

Simplify:
(2x³y)⁶

a)

2x¹⁸y⁶

b)

64x¹⁸y⁶

c)

64x³y⁶

d)

2x³y⁶

32.

Simplify:
(6p²q³)(4pq)

a)

10p³q⁴

b)

24p²q³

c)

24p³q⁴

d)

10p²q³

33.

Simplify (c⁵)(c³)(c³)

a)

c⁴⁵

b)

3c¹¹

c)

c¹¹

d)

3c⁴⁵

34.

Simplify.

(-7x³y²)²

a)

49x⁶y⁴

b)

-14x⁶y⁴

c)

-14x⁵y⁴

d)

-49x⁶y⁴

35.

Simplify.

(-2mn) (3m²n⁴)²

a)

-18m⁵n⁹

b)

-12m⁵n⁹

c)

-18m⁵n⁷

d)

-12m⁵n⁷

36.

Simplify.

3(-2x³y⁴)⁴

a)

48x¹²y¹⁶

b)

-48x¹²y¹⁶

c)

-24x¹²y¹⁶

d)

-24x⁷y⁸

37.

(r⁴)⁶

a)

10r

b)

r¹⁰

c)

24r

d)

r²⁴

Power and Product Rule

Total questions: 37

Worksheet time: 5hrs 26mins

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