Negative Exponents Of Fractional Bases Sample Problems

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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