Question

Simplify the expression. (81x^12/3x^3)^1/3

Answer 1

Raise each number to the power outside the parentheses.

$\left( \dfrac{81x^{12}}{3x^3} \right) ^{ \frac{1}{3} } = \\ = \left( 27x^{12-3} \right) ^{ \frac{1}{3} } = \\ = \left( 27x^{9} \right) ^{ \frac{1}{3} } = \\ = \left( 3^3x^{9} \right) ^{ \frac{1}{3} } = \\ = \left( 3^3 \right) ^{ \frac{1}{3} } \times \left( x^{9} \right) ^{ \frac{1}{3} } \\ = \left( 3^{3 \times \frac{1}{3} } \right) \times \left( x^{9 \times \frac{1}{3} }} \right) \\ = 3^1 x^3 \\ = 3x^3$