Easy Algebra Step-by-Step

Rules for Exponents 79

c. ()^32 y^4

Step 1. Raise each factor to the power of 4.

()^32 y )^43 ()(((( )^42 ()((yz))^44 ((()()) =xy^1284 zz

Rule for the Power of a Quotient

x

y

x

y

y

p p

p

⎛

⎝⎜

⎛⎛

⎝⎝

⎞

⎠⎟

⎞⎞

⎠⎠

=≠p,y 0

This rule tells you that a quotient raised to a power is the quotient of

each factor raised to the power.

Problem Simplify.

a.^3

4

x

⎛

⎝⎜

⎛⎛

⎝⎝

⎞

⎠⎟

⎞⎞

⎠⎠

b.

⎛−

⎝⎜

⎛⎛

⎝⎝

⎞

⎠⎟

⎞⎞

⎠⎠

4

5

3

x

y

Solution

a.^3

4

x

⎛

⎝⎜

⎛⎛

⎝⎝

⎞

⎠⎟

⎞⎞

⎠⎠

Step 1. Raise each factor to the power of 4.

3 4 4 81

x^4 x^4

⎛

⎝

⎛⎛⎛⎛

⎝⎝

⎛⎛⎛⎛ ⎞

⎠

⎞⎞⎞

⎠⎠

⎞⎞⎞⎞ =()^3

()x

=

b. −

⎛

⎝⎜

⎛⎛

⎝⎝

⎞

⎠⎟

⎞⎞

⎠⎠

4

5

3

x

y

Step 1. Raise each factor to the power of 3.

⎛−

⎝⎜

⎛⎛

⎝⎝

⎞

⎠⎟

⎞⎞

⎠⎠

=

()−

()

=

()− ()

()()

=

−

=−

4

5

64

125

64

(^33)
3
(^33) ()
3 3
3
3
x
y
x
y
x^33
125 y^3

Rules for Exponents Summary

You must be very careful when simplifying using rules for exponents. For

your convenience, here is a summary of the rules.

P