Algebra 1 Common Core Student Edition, Grade 8-9

What number
multiplied by itself
4 t im es equals 81?
9 • 9 = 81 and
(3 • 3)(3 • 3) = 81.

Think.

How can the

fractional exponent

be rewritten?

Ex p o n e n t s c a n b e

rewritten as multiple

factors if the base of

each exponential factor

is the same.

Pro b lem 4 Si m p l i f y i n g Ex p r e ssi o n s W i t h Rat i o n a l Exp o n e n t s

Simplify the expression 814.^1

81? Fi n d t h e n u m b e r t h a t w h e n m u l t i p l i e d b y i t s e l f f o u r t i m e s g i v e s 81.

81? = 3 3 • 3 • 3 • 3 = 81

Got It? 4. Simplify each expression

a. 16? b. 27? c. 64?

You can also have expressions like 92, which means 9 2 • 9 2 • 92. Consider each factor

individually. Because 9 2 = 3, you know 9 2 • 9? • 9 2 = 3 • 3 • 3 = 27. So, 9 2 = 27.

Pr o b lem 5 Si m p l i f y i n g Ex p r e ssi o n s W i t h Ra t i o n a l Exp o n e n t s

Simplify the expression 64*.^3

64^ = 645 • 64? • 645 Re w r i t e t h e e xp r e ssi o n.

= 8*8*8 Substitute 8 for 64?.

= 512 Simplify.

& Got It? 5. Simplify each expression.

a. 255 b. 27? c. 16?

You can use the properties of multiplying powers with the same base to simplify

expressions with rational exponents.

Pro p ert y Multiplying Powers With the Same Base

Words To multiply powers with the same base, add the exponents.

Algebra am • an = am+n, where a t 0 and m and n are rational numbers

Ex a m p l e s 4? • 4? = 4?+? = 4? b7 • b- 4 = b7+(- 4 ) = b3

428 Ch ap t er 7 Ex p o n e n t s a n d Ex p o n e n t i a l Fu n c t i o n s