Exponents with Fractional Bases

How to evaluate exponents with fractional bases?
Exponents with fractional bases follow the same fundamental rules of exponents as those with integer bases. The exponent indicates how many times the fractional base is multiplied by itself. The key is to remember that the exponent applies to both the numerator and the denominator of the fraction.

The following diagram shows some examples of how to evaluate exponents with fractional bases. Scroll down the page for more examples and solutions of fractions raised to a power.

Exponent Worksheets
Practice your skills with the following exponent worksheets:
Printable & Online Exponent Worksheets

Lessons on Exponents
Exponents with Different Types of Bases

For a fractional base \(\frac{a}{b}\) raised to an exponent n:

\((\frac{a}{b})^n = \frac{a^n}{b^n}\)

This means you can raise the numerator to the power of n and the denominator to the power of n separately.

Example: Evaluate \((\frac{2}{3})^3\)

\((\frac{2}{3})^3 = \frac{2^3}{3^3} = \frac{8}{27}\)

Fractions Raised to a Powers
This video provides two examples of evaluating a positive fraction raised to a power.

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Negative Fractions Raised to Powers
This video provides examples of raising negative fractions to powers.

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