Algebra 1 Common Core Student Edition, Grade 8-9

Notice the lengl
of the beach is in
kilometers. How
will you find t he
number of cubic
meters of beach
san d?

,^ /x

I, | Getting Ready!

Scien t ist s est im at e t h at t h ere are about 1020 st ars in t he universe.

A cubic meter of beach sand contains about 109 grains of sand.

Su p p o se a l l o f t h e sa n d f r o m t h e w o r l d ' s b e a c h e s i s co m b i n e d i n t o o n e

large beach, as shown below. Are t h ere more st ar s in t he universe or

grains of sand on the world's beaches? Explain your reasoning.

Not to scale

100,000 km

MATHEMATICAL

PRA CTI CES ; ---

All of the numbers in the Solve It are powers of 10. In this lesson, you will learn a

method for multiplying powers that have the same base.

Esse n t i a l U n d e r st a n d i n g You can use a property of exponents to multiply

powers with the same base.

You can write a product of powers with the same base, such as 3 4 • 32, using

one exponent.

34. 3 2 = (3. 3. 3. 3 ). (3. 3 ) = 3 6

Notice that the sum of the exponents in the expression 3^4 • 3^2 equals the exponent of 36.

In general, an equation such as 3 4 • 3 2 = 3 6 can be written using variables:

am • an = am+n.

Multiplying Powers

With the Same Base

Object ive To multiply powers with the same base

@ Common Cor e St at e St andards

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

rational exponents fo llo w s from extending the properties

o f in teger exponents to those v a lu e s...

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

Here's w h y It W orks You can use repeated multiplication to rewrite a product

of powers.

am • an = {a • a • • a) • (a • a • ... • a) = a • a • • a = a m+n

(m factors of a J (_n factors ofaj [m + n fact ors of a

c

Pow erAlg eb ra.com [ Le sso n 7- 2 Multiplying Powers With the Same Base 425