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Intermediate Algebra – Student Workbook – Second Edition 2013

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Name: _____________________<br />

Date: ________________<br />

Mini-Lesson 6a<br />

Properties of Exponents<br />

MULTIPLICATION PROPERTY OF EXPONENTS<br />

Let m, n be rational numbers. To multiply powers of the same base, keep the base & add the<br />

exponents:<br />

EXAMPLES:<br />

a) (x 2 )(x 4 )= x 2+4 = x 6<br />

b) (-3x 5 )(4x 2 )= (-3)( 4)x 5+2 = -12x 7<br />

a m a n = a m+n<br />

c) (-2a 5 )(8b 3 )(3a 2 b) = (-2)(8)(3)a 5+2 b 3+1 =-48a 7 b 4<br />

DIVISION PROPERTY OF EXPONENTS<br />

Let m, n be rational numbers. To divide powers of the same base, keep the base & subtract the<br />

exponents.<br />

m<br />

a mn<br />

a<br />

n<br />

where a 0<br />

a<br />

EXAMPLES:<br />

a) 3 15<br />

5<br />

x<br />

5 2<br />

3<br />

3<br />

3<br />

159<br />

6<br />

27<br />

b) x x<br />

2<br />

9<br />

3<br />

x<br />

c)<br />

15t<br />

2<br />

3t<br />

6<br />

15<br />

<br />

t<br />

<br />

3<br />

<br />

<br />

t<br />

6<br />

2<br />

<br />

5t<br />

<br />

62<br />

5t<br />

4<br />

7<br />

2<br />

d)<br />

4a<br />

2a<br />

5<br />

2a<br />

e) x 9<br />

cannot be simplified as the bases x and y are different<br />

5<br />

y<br />

ZERO EXPONENT a 0 = 1 if a 0<br />

EXAMPLES:<br />

3 <br />

0<br />

<br />

X <br />

a) 16 0 = 1 b) 1,<br />

X 0<br />

c) (4x) 0 = 1, x 0 d) 4x 0 = 4(1)=4, x 0<br />

e) 5(x+3) 0 = 5(1) = 5, x -3<br />

Scottsdale Community College Page 241 <strong>Intermediate</strong> <strong>Algebra</strong>

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