# Using the Rule of Exponents

by Mechelle Howard
(Houston,TX)

How do I:

1. use the rules of exponents to solve the problem shown below

2. explain the steps used simplify the expression

3. write the expression in the equivalent radical form.

(5⁴)½

### Comments for Using the Rule of Exponents

 Jul 23, 2012 Using the Rule of Exponents by: Staff The answer: There is certainly more than one way to simplify this expression. The Distributive Law of exponents applies to this problem. The Distributive law of exponents is similar to the Distributive Law used in elementary algebra. An example of the Distributive Law of elementary algebra is shown below: x * (y + z) = x * y + x * z = xy + xz The application of the Distributive Law of Exponents is very similar: (xªy³)ⁿ = xª*ⁿ y³*ⁿ = xªⁿ y³ⁿ When the Distributive Law of Exponents is applied to your problem (5⁴)^(½) = 5^(4*½) = 5² = 25 >>> the final answer is: 5² = 25 You can also simplify this expression using the radical notation: (5⁴)^(½) = √(5⁴) = √(5² * 5²) = 5² = 25 Or, alternatively (5⁴)^(½) = √(5⁴) = √(625) = 25 Thanks for writing. Staff www.solving-math-problems.com