How to Solve Rational Exponents

Before solving a problem containing rational exponents, you must first have firm understanding of powers and roots. For example, 2 to the second power---or 2 squared---equals 4. The second root---or square root---of 4 equals 2. More importantly, you must also understand rules for exponents. The power rule for exponents states that (a^b)^c equals a^(b*c). Since a rational number has the form b/c, you can rewrite it as b*(1/c). In terms of exponents, this is the b-th power times the c-th root.

Difficulty: Moderately Easy

Instructions

Things You'll Need:

• Calculator

1. Write the rational exponent in the form "b*(1/c)." For example:
   
   4^(3/2) = 4^[3*(1/2)]

2. Use the power rule to rewrite the problem as a root raised to a power.
   
   4^[3*(1/2)] = [4^(1/2)]^3

3. Evaluate the root.
   
   [4^(1/2)]^3 = 2^3

4. Evaluate the power.
   
   2^3 = 8

Tips & Warnings

• Some problems are easier to evaluate as a root raised to a power, while others are easier as a power raised to a root. The multiplication rule allows either one to be used, so choose the one that best fits the problem.

References

• West Texas A&M University Beginning Algebra Tutorial

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