Free Printable Laws of Exponents: Product to a Power

1.

Which is the correct rule for raising a product to a power?

a)

For every non-zero number, a and b and integer, n: $\left(ab\right)^n=ab^n$

b)

For every non-zero number, a and b and integer, n: $\left(ab\right)^n=a^nb^{ }$

c)

For every non-zero number, a and b and integer, n: $\left(ab\right)^n=a^nb^n$

d)

For every non-zero number, a and b and integer, n: $\left(ab\right)^n=\frac{1}{a^nb^n}$

2.

Simplify: $\left(5a\right)^2$

a)

$5^2a^2$

b)

$25a^2$

c)

$5a^2$

d)

$5^2a$

3.

Simplify: $\left(2x^2\right)^3$

a)

$2x^6$

b)

$2x^5$

c)

$2^3x^6$

d)

$8x^6$

4.

Simplify: $\left(v^3w^4\right)^5$

a)

$v^8w^9$

b)

$v^{15}w^{20}$

c)

$vw^{35}$

d)

$v^2w$

5.

Simplify: $\left(4c^3\right)^{-2}$

a)

$4^{-2}c^{-6}$

b)

$\frac{1}{4^2c^6}$

c)

$\frac{4}{c^6}$

d)

$\frac{1}{16c^6}$

6.

Simplify: $\left(6x^{-3}\right)^{-2}$

a)

$\frac{x^6}{6^2}$

b)

$\frac{1}{6x^6}$

c)

$6x^6$

d)

$\frac{x^6}{36}$

7.

Simplify: $\left(6x^{-3}\right)^{-2}$

a)

$\frac{x^6}{6^2}$

b)

$6x^6$

c)

$\frac{1}{6x^6}$

d)

$\frac{x^6}{36}$

8.

Simplify: $\left(2x^5\cdot4y^6\right)^2$

a)

$2x^{10}\cdot4y^{12}$

b)

$2^2x^{10}\cdot4^2y^{12}$

c)

$4x^{10}\cdot16y^{12}$

d)

$64x^{10}y^{12}$

9.

Simplify: $\left(3p^3\cdot2p^{-7}\right)^{-3}$

a)

$6^{-3}p^{-9}p^{21}$

b)

$6^{-3}p^{12}$

c)

$\frac{p^{12}}{6^3}$

d)

$\frac{p^{12}}{216}$

10.

Now go complete page 9 of the Laws of Exponents Tiered Practice in Schoology.

a)

Use your notes!

b)

No calculators!

c)

Good Luck!

Laws of Exponents: Product to a Power

Total questions: 10

Worksheet time: 10mins

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