# Law of Exponent

by Sharina
(Philippines)

Simplify the following expression.

8x9/2x5=

Options:

1. Factor both both the numerator and denominator. The common factors can be canceled.

2. Simplify the expression by subtracting the exponents.

### Comments for Law of Exponent

 Oct 14, 2011 Reducing Fractions with Exponents by: Staff Question: by Sharina (Philippines) 8x9/2x5= Answer: 8x⁹ / 2x⁵ = This fraction can be simplified by subtracting the exponents: 8x⁹ / 2x⁵ = 2³x⁹ / 2¹x⁵ = 2⁽³⁻¹⁾x⁽⁹⁻⁵⁾ = 2⁽²⁾x⁽⁴⁾ = 2²x⁴ = 4x⁴ However, to understand the process, it’s probably helpful to factor both the numerator and denominator. The common factors can be canceled: 8 = 2 * 2 * 2 x⁹ = x * x * x * x * x * x * x * x * x 2 = 1 * 2 x⁵ = x * x * x * x * x 2 * 2 * 2 *x⁹ / 2x⁵ = 8 = 2 * 2 * 2 8x⁹ / 2x⁵ = [(2 * 2 * 2) * (x * x * x * x * x * x * x * x * x)] / [(2) * (x * x * x * x * x)] Factors which appear in the numerator AND denominator can be canceled: = [(2 * 2) * (x * x * x * x)] * (2 / 2) * (x / x) * (x / x) * (x / x) * (x / x) * (x / x) = [(2 * 2) * (x * x * x * x)] * (1) * (1) * (1) * (1) * (1) * (1) = [(2 * 2) * (x * x * x * x)] = (2²) * (x⁴) = 4 * x⁴ = 4x⁴ The final answer is: 4x⁴ Thanks for writing. Staff www.solving-math-problems.com