# ZERO AND NEGATIVE EXPONENTS

## Zero Exponent

Words :

Any nonzero number raised to the zero power is 1.

Numbers :

50  =  1

(-5)0  =  1

2150  =  1

(2/3)0  =  1

Algebra :

If x ≠ 0, then x0 = 1.

## Negative Exponent

Words :

Any nonzero number raised to a negative exponent is equal to 1 divided by that number raised to the opposite (positive) exponent.

Numbers :

5-2  =  1/5=  1/25

2-4  =  1/24  =  1/16

Algebra :

If x ≠ 0 and n is an integer, then x-n = 1/xn

## Solved Examples

Example 1 :

Simplify :

5-3

Solution :

=  5-3

=  1 / 53

=  1 / (5 ⋅ 5 ⋅ 5)

=  1/125

Example 2 :

Simplify :

80

Solution :

=  80

Any non zero number raised to the zero power is 1.

=  1

Example 3 :

Simplify :

(-2)-4

Solution :

=  (-2)-4

=  1 / (-2)4

=  1 / [(-2)(-2)(-2)(-2)]

=  1/16

Example 4 :

Simplify :

-3-4

Solution :

=  -3-4

=  -1 / 34

=  -1 / (3 ⋅ 3 ⋅ 3 ⋅ 3)

=  -1/81

Example 5 :

Evaluate y-1 for y = 2.

Solution :

=  y-1

Substitute 2 for y.

=  2-1

=  1/2

Example 6 :

Evaluate a0b-3 for a = 8 and b = -2.

Solution :

=  a0b-3

Substitute 8 for a and -2 for b.

=  8⋅ (-2)-3

=  1 ⋅ 1/(-2)3

=  1 ⋅ 1 / [(-2)(-2)(-2)]

=  1 ⋅ 1 / (-8)

=  1 ⋅ (-1/8)

=  -1/8

Example 7 :

Simplify :

5a-2

Solution :

=  5a-2

=  5 ⋅ 1/a2

=  5/a2

Example 8 :

Simplify :

-5/p-4

Solution :

=  -5/p-4

=  -5 ⋅ 1/p-4

=  -5 ⋅ p4

=  -5p4

Example 9 :

Simplify :

x-2/a0y3

Solution :

=  x-2/a0y3

=  1 / (x2 ⋅ 1 ⋅ y3)

=  1/x2y3

Example 10 :

Simplify :

3p0n-5

Solution :

=  3p0n-5

=  3 ⋅ 1 ⋅ 1/n5

=  3/n5 Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

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