Free Printable Powers of Products and Quotients

1.

Which of the following is the correct way to simplify this expression?
$\left(a^mb^n\right)^p$

a)

$ab^{m\cdot n\cdot p}$

b)

$a^{m\cdot p}\ b^{n\cdot p}$

c)

$a^mb^n$

2.

What's our "shortcut" for thinking of this property?
$\left(a^mb^n\right)^p\ =\ a^{mp}\ b^{np}$

a)

It's like "distributing" the power

b)

We add the powers together

c)

We divide the powers

3.

Simplify the following:
$\left(r^7s^3\right)^3$

a)

$r^7s^9$

b)

$r^{21}s^9$

c)

$r^{21}s^3$

4.

Simplify the following:
$\left(abc^5\right)^5$

a)

$a^5b^5c^{25}$

b)

$a^5b^5c^5$

c)

$abc^{25}$

5.

Simplify the following:
$\left(4x^3y^2\right)^2$

a)

$16x^3y^2$

b)

$4x^6y^4$

c)

$16x^6y^4$

6.

Simplify the following:
$\left(x^2y^4m^3\right)^8$

a)

$x^{10}y^{12}m^{11}$

b)

$x^6y^{-4}m^{-5}$

c)

$x^{16}y^{32}m^{24}$

7.

Which of the following is the correct way to simplify this expression?
$\left(\frac{a^m}{b^n}\right)^p$

a)

$\frac{a^{m\cdot p}}{b^{n\cdot p}}$

b)

$\frac{a^m+a^p}{b^n+b^p}$

c)

$a^{m\cdot p}\ b^{n\cdot p}$

8.

What's our "shortcut" for thinking of this property?
$\left(\frac{a^m}{b^n}\right)^{p\ }=\ \frac{a^{mp}}{b^{np}}$

a)

It's like "distributing" the power to each part of the top and bottom

b)

We subtract m and n, then multiply by p

c)

We exponent-ize everything

9.

Simplify the following:
$\left(\frac{x^2}{y^3}\right)^4$

a)

$\frac{x^8}{y^{12}}$

b)

$\frac{x^6}{y^7}$

c)

$x^8y^{12}$

10.

Simplify the following:
$\left(\frac{x^2y}{z^3}\right)^5$

a)

$\frac{x^{10}y^5}{z^{15}}$

b)

$\frac{x^{10}y}{z^{15}}$

c)

$\frac{x^{10}y}{z^3}$

11.

Simplify the following:
$\left(\frac{3x^3}{5y}\right)^2$

a)

$\frac{9x^6}{25y^2}$

b)

$\frac{9x^3}{25y}$

c)

$\frac{9x^6}{5y}$

12.

Simplify the following:
$\left(\frac{h^7}{4}\right)^3$

a)

$\frac{h^{21}}{4^3}$

b)

$64h^{21}$

c)

$\frac{h^{21}}{4}$

Powers of Products and Quotients

Total questions: 12

Worksheet time: 1hrs 4mins

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