Algebra Examples

${(- 2)}^{4} {(6 x^{- 3})}^{- 2}$

Step 1

Raise $- 2$ to the power of $4$ .

$16 {(6 x^{- 3})}^{- 2}$

Step 2

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

$16 {(6 \frac{1}{x^{3}})}^{- 2}$

Step 3

Combine $6$ and $\frac{1}{x^{3}}$ .

$16 {(\frac{6}{x^{3}})}^{- 2}$

Step 4

Change the sign of the exponent by rewriting the base as its reciprocal.

$16 {(\frac{x^{3}}{6})}^{2}$

Step 5

Simplify the expression.

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Step 5.1

Apply the product rule to $\frac{x^{3}}{6}$ .

$16 \frac{{(x^{3})}^{2}}{6^{2}}$

Step 5.2

Multiply the exponents in ${(x^{3})}^{2}$ .

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Step 5.2.1

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

$16 \frac{x^{3 \cdot 2}}{6^{2}}$

Step 5.2.2

Multiply $3$ by $2$ .

$16 \frac{x^{6}}{6^{2}}$

Step 5.3

Raise $6$ to the power of $2$ .

$16 \frac{x^{6}}{36}$

Step 6

Cancel the common factor of $4$ .

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Step 6.1

Factor $4$ out of $16$ .

$4 (4) \frac{x^{6}}{36}$

Step 6.2

Factor $4$ out of $36$ .

$4 \cdot 4 \frac{x^{6}}{4 \cdot 9}$

Step 6.3

Cancel the common factor.

$4 \cdot 4 \frac{x^{6}}{4 \cdot 9}$

Step 6.4

Rewrite the expression.

$4 \frac{x^{6}}{9}$

Step 7

Combine $4$ and $\frac{x^{6}}{9}$ .

$\frac{4 x^{6}}{9}$