How can you write \frac{1}{\sqrt[3]{-12} } in a^(b) format without any radicals?

Question

how can you write
`\frac{1}{\sqrt[3]{-12} }` in
`a^(b)` format without any radicals?

Answer 1

`\displaystyle (-12)^{-(1)/(3)}`

General Formulas and Concepts:

Algebra I

• Exponential Rule [Rewrite]:
  `\displaystyle b^(-m) = (1)/(b^m)`
• Exponential Rule [Root Rewrite]:
  `\displaystyle \sqrt[n]{x} = x^{(1)/(n)}`

Explanation:

Step 1: Define

`\displaystyle \frac{1}{\sqrt[3]{-12}}`

Step 2: Rewrite

1. Exponential Rule - Root Rewrite:
   `\displaystyle \frac{1}{(-12)^{(1)/(3)}}`
2. Exponential Rule - Rewrite:
   `\displaystyle (-12)^{-(1)/(3)}`