Question

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

Answer 1

Raise each number to the power outside the parentheses.


`\left( (81x^(12))/(3x^3) \right) ^{ (1)/(3) } = \\ = \left( 27x^(12-3) \right) ^{ (1)/(3) } = \\ = \left( 27x^(9) \right) ^{ (1)/(3) } = \\ = \left( 3^3x^(9) \right) ^{ (1)/(3) } = \\ = \left( 3^3 \right) ^{ (1)/(3) } * \left( x^(9) \right) ^{ (1)/(3) } \\ = \left( 3^{3 * (1)/(3) } \right) * \left( x^{9 * (1)/(3) }} \right) \\ = 3^1 x^3 \\ = 3x^3`