Algebra Examples

${(9 x^{- 5})}^{3}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(9 \frac{1}{x^{5}})}^{3}$

Step 2

Combine $9$ and $\frac{1}{x^{5}}$ .

${(\frac{9}{x^{5}})}^{3}$

Step 3

Simplify the expression.

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Step 3.1

Apply the product rule to $\frac{9}{x^{5}}$ .

$\frac{9^{3}}{{(x^{5})}^{3}}$

Step 3.2

Raise $9$ to the power of $3$ .

$\frac{729}{{(x^{5})}^{3}}$

Step 3.3

Multiply the exponents in ${(x^{5})}^{3}$ .

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Step 3.3.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{729}{x^{5 \cdot 3}}$

Step 3.3.2

Multiply $5$ by $3$ .

$\frac{729}{x^{15}}$