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Here are some tips for Negative Exponents Of Fractional Bases, which aligns with New York state standards:

Negative Exponents Of Fractional Bases


For this topic, you will need to know how to solve exponents with fractions.
To review the Exponents Of Fractional Bases topic, see here.

A negative exponent means a reciprocal.

x-n = 1
xn
OR 1 ÷ xn


Example 1:

Evaluate the following. If the answer is a whole number, just input the whole number. Express fractions as 'numerator/denominator'. i.e. '5/7'. Also use improper fractions and not mixed fractions in your answer.
( 1
4
) -1

When the exponent is -1, the answer is the reciprocal of the base.
( 1
4
) -1
=
1 ÷ ( 1
4
) 1
=
1 × ( 4
1
) 1
= 41 = 4 
The answer is


Example 2:

Evaluate the following. If the answer is a whole number, just input the whole number. Express fractions as 'numerator/denominator'. i.e. '5/7'. Also use improper fractions and not mixed fractions in your answer.
( 5
4
) -2

( 5
4
) -2
=
1 ÷ ( 5
4
) 2
=
1 × ( 4
5
) 2
=
42
52
= 16
25
The answer is

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