Basic Math Examples

$(u^{3} w^{- 1}) {(\frac{u^{- 4} v}{3 w^{- 3}})}^{2}$

Step 1

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

$u^{3} \frac{1}{w} {(\frac{u^{- 4} v}{3 w^{- 3}})}^{2}$

Step 2

Combine $u^{3}$ and $\frac{1}{w}$ .

$\frac{u^{3}}{w} {(\frac{u^{- 4} v}{3 w^{- 3}})}^{2}$

Step 3

Simplify.

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Step 3.1

Move $u^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{u^{3}}{w} {(\frac{v}{3 w^{- 3} u^{4}})}^{2}$

Step 3.2

Move $w^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{u^{3}}{w} {(\frac{v w^{3}}{3 u^{4}})}^{2}$

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 $\frac{v w^{3}}{3 u^{4}}$ .

$\frac{u^{3}}{w} \cdot \frac{{(v w^{3})}^{2}}{{(3 u^{4})}^{2}}$

Step 4.2

Apply the product rule to $v w^{3}$ .

$\frac{u^{3}}{w} \cdot \frac{v^{2} {(w^{3})}^{2}}{{(3 u^{4})}^{2}}$

Step 4.3

Apply the product rule to $3 u^{4}$ .

$\frac{u^{3}}{w} \cdot \frac{v^{2} {(w^{3})}^{2}}{3^{2} {(u^{4})}^{2}}$

Step 5

Combine fractions.

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Step 5.1

Combine.

$\frac{u^{3} (v^{2} {(w^{3})}^{2})}{w (3^{2} {(u^{4})}^{2})}$

Step 5.2

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

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Step 5.2.1

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

$\frac{u^{3} v^{2} w^{3 \cdot 2}}{w \cdot 3^{2} {(u^{4})}^{2}}$

Step 5.2.2

Multiply $3$ by $2$ .

$\frac{u^{3} v^{2} w^{6}}{w \cdot 3^{2} {(u^{4})}^{2}}$

Step 6

Simplify the denominator.

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Step 6.1

Raise $3$ to the power of $2$ .

$\frac{u^{3} v^{2} w^{6}}{w \cdot 9 {(u^{4})}^{2}}$

Step 6.2

Multiply the exponents in ${(u^{4})}^{2}$ .

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Step 6.2.1

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

$\frac{u^{3} v^{2} w^{6}}{w \cdot 9 u^{4 \cdot 2}}$

Step 6.2.2

Multiply $4$ by $2$ .

$\frac{u^{3} v^{2} w^{6}}{w \cdot 9 u^{8}}$

Step 7

Reduce the expression by cancelling the common factors.

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Step 7.1

Cancel the common factor of $u^{3}$ and $u^{8}$ .

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Step 7.1.1

Factor $u^{3}$ out of $u^{3} v^{2} w^{6}$ .

$\frac{u^{3} (v^{2} w^{6})}{w \cdot 9 u^{8}}$

Step 7.1.2

Cancel the common factors.

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Step 7.1.2.1

Factor $u^{3}$ out of $w \cdot 9 u^{8}$ .

$\frac{u^{3} (v^{2} w^{6})}{u^{3} (w \cdot 9 u^{5})}$

Step 7.1.2.2

Cancel the common factor.

$\frac{u^{3} (v^{2} w^{6})}{u^{3} (w \cdot 9 u^{5})}$

Step 7.1.2.3

Rewrite the expression.

$\frac{v^{2} w^{6}}{w \cdot 9 u^{5}}$

Step 7.2

Cancel the common factor of $w^{6}$ and $w$ .

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Step 7.2.1

Factor $w$ out of $v^{2} w^{6}$ .

$\frac{w (v^{2} w^{5})}{w \cdot 9 u^{5}}$

Step 7.2.2

Cancel the common factors.

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Step 7.2.2.1

Factor $w$ out of $w \cdot 9 u^{5}$ .

$\frac{w (v^{2} w^{5})}{w (9 u^{5})}$

Step 7.2.2.2

Cancel the common factor.

$\frac{w (v^{2} w^{5})}{w (9 u^{5})}$

Step 7.2.2.3

Rewrite the expression.

$\frac{v^{2} w^{5}}{9 u^{5}}$