Negative Exponents Of Fractional Bases Sample Problems

Math Practice Online > free > lessons > New York > 9th grade > Negative Exponents Of Fractional Bases

If your child needs math practice, click here.

For sample problems, click here.
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