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Algebra 1
Section 8.2
Negative and Zero
Exponents
For an expression to be completely simplified, there must be
no negative exponents
To make a negative exponent positive:
- move it (the factor) up if it is in the denominator
or
- move it (the factor) down if it is in the numerator
3-2
=1
32
=1
9
1
3-2
3-2
2-3
= 32
= 23
32
=8
9
=9
3x -5
= 3
x5
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Rewrite the expression using positive exponents.
1. x –7
2. 5x - 4
=1
x7
= 5
x4
3. 1
2x -3
= x3
2 only move x - 3 up
only move the x - 4 down, it is the only one with
a negative exponent
4. x –2 y3
= y3
x2
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5. 3x –3 y –8
= 3
x3y8
6.
only move x - 3 and y – 8 down, the 3 does not have a negative exponent
1
7x – 4 y -1
= x4y
7
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Evaluate the expression.
7. 3-2
= 1
32
=1
9
8. - 40 · 1
2 -2
= -1 · 22
= -1(4)
=-4
Anything to the zero power equals 1.
30
=1
x0
=1
(-5)0
=1
-30
= -1
0
=1
9. 63 · 6-1
= 62 multiplying with same base, add exponents
= 36
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10. 7-9 · 79
= 70 when multiplying with same base, add exponents
=1
11. (- 4 –2) –1
= - 42
= -16
power to a power, multiply exponents
12. 5 · 5 –1
= 50 when multiplying with same base, add exponents
= 1 anything to zero power equals 1
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Rewrite the expression using positive exponents.
13. (-3)0 x
= 1· x
=x
15. (-3x) –1 · 2y
= 2y
-3x
14. (-2x) -3
= 1
(-2x)3
= 1
-8x3
16. (3x) -1
= 1
3x
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17. 4
b -2
= 4b2
18.
1
(4x) -3
= (4x)3
= 64x3
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Algebra 1
Section 8.2
Assignment
Rewrite the expression using positive exponents.
1.) x – 7
2.) 5x – 4
3.)
4.) x – 2 y3
5.) 3x – 3 y – 8
6.)
1
2x - 3
1
7x - 4 y 1
Evaluate the expression.
1
7.) 3 – 2
8.) - 40 
10.) 7-9 · 79
11.) (- 4-2) -1
2
2
9.) 63 · 6 -1
12.) 5 · 5 -1
Rewrite the expression using positive exponents.
13.) (-3)0 x
14.) (-2x) -3
16.) (3x) -1
17.)
4
b 2
15.) (-3x) -1 · 2y
18.)
1
(4x)  3
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