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Solution assignment 08 Rules for exponents

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Assignment 8

Simplify:

[(\displaystyle\frac{x}{3})^3.\displaystyle\frac{8}{x^{-2}}]^{-3}

Solution

We work from inside out and use the rules for exponents:

[(\displaystyle\frac{x}{3})^3.\displaystyle\frac{8}{x^{-2}}]^{-3}=[\displaystyle\frac{x^3}{2^3}8x^2]^{-3}=[\displaystyle\frac{8x^5}{8}]^{-3}=x^{-15}

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