Algebra Examples

${(\frac{2 u^{- 5} v^{2}}{8 w})}^{- 2}$

Step 1

Move $u^{- 5}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{2 v^{2}}{8 w u^{5}})}^{- 2}$

Step 2

Cancel the common factor of $2$ and $8$ .

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Step 2.1

Factor $2$ out of $2 v^{2}$ .

${(\frac{2 (v^{2})}{8 w u^{5}})}^{- 2}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $2$ out of $8 w u^{5}$ .

${(\frac{2 (v^{2})}{2 (4 w u^{5})})}^{- 2}$

Step 2.2.2

Cancel the common factor.

${(\frac{2 v^{2}}{2 (4 w u^{5})})}^{- 2}$

Step 2.2.3

Rewrite the expression.

${(\frac{v^{2}}{4 w u^{5}})}^{- 2}$

Step 3

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

${(\frac{4 w u^{5}}{v^{2}})}^{2}$

Step 4

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 4.1

Apply the product rule to $\frac{4 w u^{5}}{v^{2}}$ .

$\frac{{(4 w u^{5})}^{2}}{{(v^{2})}^{2}}$

Step 4.2

Apply the product rule to $4 w u^{5}$ .

$\frac{{(4 w)}^{2} {(u^{5})}^{2}}{{(v^{2})}^{2}}$

Step 4.3

Apply the product rule to $4 w$ .

$\frac{4^{2} w^{2} {(u^{5})}^{2}}{{(v^{2})}^{2}}$

Step 5

Simplify the numerator.

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Step 5.1

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

$\frac{16 w^{2} {(u^{5})}^{2}}{{(v^{2})}^{2}}$

Step 5.2

Multiply the exponents in ${(u^{5})}^{2}$ .

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Step 5.2.1

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

$\frac{16 w^{2} u^{5 \cdot 2}}{{(v^{2})}^{2}}$

Step 5.2.2

Multiply $5$ by $2$ .

$\frac{16 w^{2} u^{10}}{{(v^{2})}^{2}}$

Step 6

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

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Step 6.1

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

$\frac{16 w^{2} u^{10}}{v^{2 \cdot 2}}$

Step 6.2

Multiply $2$ by $2$ .

$\frac{16 w^{2} u^{10}}{v^{4}}$