Algebra 1 Common Core Student Edition, Grade 8-9

Object ives To divide powers with the same base

To raise a quotient to a power

1 Getting Ready!

So l v e a si m p l e r
problem f i r st. Use
a val ue f o r x t o
understand all of
the relationships
in t h is problem.

A machine makes wooden dowels by removing m at erial from a block

of wood as shown in the diagram. What percent of the wood does

the machine remove from the original piece of wood to form the

dowel? Explain how you found your answer. (H in t : W hat is t he

volume o f t h e d o wel?)

, M A TH EM A TI CA L

I PRA CT I CES

Division Properties of

Ex p o n e n t s

W

@ Common Core State Standards

N -R N .A .1 Explain h o w th e d e fin itio n o f the meaning of

rational exponents fo llo w s from extending the properties

o f in teger exponents to those values, allow ing fo r a

n o tation fo r radicals in term s o f rational exponents.

MP 1, MP 2, MP 3, MP 4, MP 7

In the Solve It, the expression for the volume of the dowel involves a quotient raised to

a power.

Esse n t i a l U n d e r st a n d i n g You can use properties of exponents to divide powers

with the same base.

You can use repeated multiplication to simplify quotients of powers with the same base.

Expand the numerator and the denominator. Then divide out the common factors.

45 _ jf 4 -4 = 42

43...

This example suggests the following property of exponents.

pr0perty Dividing Powers With the Same Base

Words To divide powers with the same base, subtract the exponents.

Algebra nm = am n,— where a =t= 0 and m and n are rational numbers

Ex a m p l e s ^ = ?6 2 6~ 2 = 2G 1 4 A ^ X 4 = xA - 7 47 —^ = x 3 = -^^1 -r = S* S4 2 3_L 3-2 I = i. 4 = S4

r 2 x7 x &

c

Po w erAlg eb ra.com | Lesso n 7-4 Division Propert ies o f Exponent s __________ 439