7th Grade Math

178 Rational Numbers

Quotient of Powers

Words To divide powers with the same base, subtract their

exponents.

Symbols a

m

_an = am - n, where a ≠ 0

Example 4

5

_

42

= 45 -^2 or 4^3

Divide Powers

Find each quotient. Express using exponents.

5

7

_

54

_^57

54

= 57 -^4 The common base is 5.

= 53 Subtract the exponents.

y^5

_

y^3

y^5

_

y^3

= y^5 -^3 The common base is y.

= y^2 Subtract the exponents.

Simplify. Express using exponents.

e.^7

6

_

72

f.^9 c

7

_

3 c^2

COMPUTERS The table compares the

Year

Processing Speed

(instructions per

second)

1999 103

2008 109

processing speeds of a specific type of

computer in 1999 and in 2008. Find how

many times faster the computer was in

2008 than in 1999.

Write a division expression to compare the speeds.

10

9

_

103

= 109 -^3 The common base is 10.

= 106 Subtract the exponents.

So, the computer was 10^6 or one million times faster in 2008 than

in 1999.

g. FOOD A candy store owner has 3^8 chocolate bars and

36 packages of sour candy. How many times as many

chocolate bars does the candy store owner have than

packages of sour candy?

Real-World Link

According to a recent

survey, 75% of adults

prefer E-mail to

instant messaging.

Meanwhile, 75% of

teens prefer instant

messaging to E-mail.

RR

A

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