Basic Math Examples

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

Step 1

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

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

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $- 2 u^{3} v w^{2}$ .

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

Step 2.2

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

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Step 2.2.1

Apply the product rule to $- 2 u^{3} v$ .

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

Step 2.2.2

Apply the product rule to $- 2 u^{3}$ .

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

Step 2.3

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

$u v^{3} \frac{1}{- 8 {(u^{3})}^{3} v^{3} {(w^{2})}^{3}}$

Step 2.4

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

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Step 2.4.1

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

$u v^{3} \frac{1}{- 8 u^{3 \cdot 3} v^{3} {(w^{2})}^{3}}$

Step 2.4.2

Multiply $3$ by $3$ .

$u v^{3} \frac{1}{- 8 u^{9} v^{3} {(w^{2})}^{3}}$

Step 2.5

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

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Step 2.5.1

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

$u v^{3} \frac{1}{- 8 u^{9} v^{3} w^{2 \cdot 3}}$

Step 2.5.2

Multiply $2$ by $3$ .

$u v^{3} \frac{1}{- 8 u^{9} v^{3} w^{6}}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

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

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Step 3.1.1

Factor $u v^{3}$ out of $- 8 u^{9} v^{3} w^{6}$ .

$u v^{3} \frac{1}{u v^{3} (- 8 u^{8} w^{6})}$

Step 3.1.2

Cancel the common factor.

$u v^{3} \frac{1}{u v^{3} (- 8 u^{8} w^{6})}$

Step 3.1.3

Rewrite the expression.

$\frac{1}{- 8 u^{8} w^{6}}$

Step 3.2

Move the negative in front of the fraction.

$- \frac{1}{8 u^{8} w^{6}}$