Algebra 1 Common Core Student Edition, Grade 8-9

Make a plan. What
do you need t o
know b ef o re you
can u se t h e volume
formula?

MATHEMATICAL

PRA CTICES

% Getting Ready!

The radius o f a bubble made by t he bubble machine on t he rig ht is

2.5 times as large as the radius of a bubble made by the bubble

machine on the lef t. What is the volume of a bubble made by the

machine on t he rig ht? Explain your reasoning. (Hin t : V = j 7 rr3)

radius = x in.

Object ives To raise a power to a power

To raise a product to a power

More Multiplication

Pr o p er t i es o f Exp o n en t s

Co m m o n Co r e St at e St a n d a r d s

N-RN.A.1 Explain ho w the d e fin ition o f the meaning o f

rational exponents fo llo w s from extending th e properties

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

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

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

In the Solve It, the expression for the volume of the larger bubble involves a product

raised to a power. In this lesson, you will use properties of exponents to simplify similar

expressions.

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 simplify a

power raised to a power or a product raised to a power.

You can use repeated multiplication to simplify a power raised to a power.

(X 5) 2 = X 5 • X 5 = X 5+ 5 = X 5' 2 = X 10

Notice that (x5) 2 = x5‘2. Raising a power to a power is the same as raising the base to

the product of the exponents.

Pro p ert y Raising a Power to a Power

Words To raise a power to a power, multiply the exponents.

Algebra {am)n = a mn, where a ± 0 and to and n are rational numbers

Ex a m p l e s (54) 2 = 54’ 2 = 5 8 (to3) 5 = to3' 5 = to 15

,( 3. 0 to)'3 = TO 3 = f l 2 3. 0 9 , 1 , 3 ( X 2 p = X2 5 = JC101. 3 3_

0

Po w erAlg eb ra.com | Lesso n 7- 3 More Multiplication Properties of Exponents 433