Basic Math Examples

$\frac{{(- u^{3} n^{- 5})}^{- 4}}{{(u n)}^{- 1}}$

Step 1

Simplify the expression.

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Step 1.1

Move ${(- u^{3} n^{- 5})}^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{{(u n)}^{- 1} {(- u^{3} n^{- 5})}^{4}}$

Step 1.2

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

$\frac{u n}{{(- u^{3} n^{- 5})}^{4}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $- u^{3} n^{- 5}$ .

$\frac{u n}{{(- u^{3})}^{4} {(n^{- 5})}^{4}}$

Step 2.2

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

$\frac{u n}{{(- 1)}^{4} {(u^{3})}^{4} {(n^{- 5})}^{4}}$

Step 2.3

Raise $- 1$ to the power of $4$ .

$\frac{u n}{1 {(u^{3})}^{4} {(n^{- 5})}^{4}}$

Step 2.4

Multiply ${(u^{3})}^{4}$ by $1$ .

$\frac{u n}{{(u^{3})}^{4} {(n^{- 5})}^{4}}$

Step 2.5

Multiply the exponents in ${(u^{3})}^{4}$ .

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Step 2.5.1

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

$\frac{u n}{u^{3 \cdot 4} {(n^{- 5})}^{4}}$

Step 2.5.2

Multiply $3$ by $4$ .

$\frac{u n}{u^{12} {(n^{- 5})}^{4}}$

Step 2.6

Multiply the exponents in ${(n^{- 5})}^{4}$ .

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Step 2.6.1

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

$\frac{u n}{u^{12} n^{- 5 \cdot 4}}$

Step 2.6.2

Multiply $- 5$ by $4$ .

$\frac{u n}{u^{12} n^{- 20}}$

Step 2.7

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

$\frac{u n}{u^{12} \frac{1}{n^{20}}}$

Step 3

Combine $u^{12}$ and $\frac{1}{n^{20}}$ .

$\frac{u n}{\frac{u^{12}}{n^{20}}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$u n \frac{n^{20}}{u^{12}}$

Step 5

Cancel the common factor of $u$ .

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Step 5.1

Factor $u$ out of $u n$ .

$u (n) \frac{n^{20}}{u^{12}}$

Step 5.2

Factor $u$ out of $u^{12}$ .

$u (n) \frac{n^{20}}{u \cdot u^{11}}$

Step 5.3

Cancel the common factor.

$u n \frac{n^{20}}{u \cdot u^{11}}$

Step 5.4

Rewrite the expression.

$n \frac{n^{20}}{u^{11}}$

Step 6

Combine $n$ and $\frac{n^{20}}{u^{11}}$ .

$\frac{n \cdot n^{20}}{u^{11}}$

Step 7

Multiply $n$ by $n^{20}$ by adding the exponents.

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Step 7.1

Multiply $n$ by $n^{20}$ .

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Step 7.1.1

Raise $n$ to the power of $1$ .

$\frac{n^{1} n^{20}}{u^{11}}$

Step 7.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{n^{1 + 20}}{u^{11}}$

Step 7.2

Add $1$ and $20$ .

$\frac{n^{21}}{u^{11}}$