Basic Math Examples

${(\frac{5 m^{4} n^{- 1}}{3 n^{- 6} m^{- 4}})}^{- 2}$

Step 1

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

${(\frac{5 m^{4} n^{- 1} m^{4}}{3 n^{- 6}})}^{- 2}$

Step 2

Move $n^{- 6}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(\frac{5 m^{4} n^{- 1} m^{4} n^{6}}{3})}^{- 2}$

Step 3

Simplify the numerator.

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Step 3.1

Multiply $m^{4}$ by $m^{4}$ by adding the exponents.

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Step 3.1.1

Move $m^{4}$ .

${(\frac{5 (m^{4} m^{4}) n^{- 1} n^{6}}{3})}^{- 2}$

Step 3.1.2

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

${(\frac{5 m^{4 + 4} n^{- 1} n^{6}}{3})}^{- 2}$

Step 3.1.3

Add $4$ and $4$ .

${(\frac{5 m^{8} n^{- 1} n^{6}}{3})}^{- 2}$

Step 3.2

Multiply $n^{- 1}$ by $n^{6}$ by adding the exponents.

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Step 3.2.1

Move $n^{6}$ .

${(\frac{5 m^{8} (n^{6} n^{- 1})}{3})}^{- 2}$

Step 3.2.2

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

${(\frac{5 m^{8} n^{6 - 1}}{3})}^{- 2}$

Step 3.2.3

Subtract $1$ from $6$ .

${(\frac{5 m^{8} n^{5}}{3})}^{- 2}$

Step 4

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

${(\frac{3}{5 m^{8} n^{5}})}^{2}$

Step 5

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

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Step 5.1

Apply the product rule to $\frac{3}{5 m^{8} n^{5}}$ .

$\frac{3^{2}}{{(5 m^{8} n^{5})}^{2}}$

Step 5.2

Apply the product rule to $5 m^{8} n^{5}$ .

$\frac{3^{2}}{{(5 m^{8})}^{2} {(n^{5})}^{2}}$

Step 5.3

Apply the product rule to $5 m^{8}$ .

$\frac{3^{2}}{5^{2} {(m^{8})}^{2} {(n^{5})}^{2}}$

Step 6

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

$\frac{9}{5^{2} {(m^{8})}^{2} {(n^{5})}^{2}}$

Step 7

Simplify the denominator.

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Step 7.1

Raise $5$ to the power of $2$ .

$\frac{9}{25 {(m^{8})}^{2} {(n^{5})}^{2}}$

Step 7.2

Multiply the exponents in ${(m^{8})}^{2}$ .

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Step 7.2.1

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

$\frac{9}{25 m^{8 \cdot 2} {(n^{5})}^{2}}$

Step 7.2.2

Multiply $8$ by $2$ .

$\frac{9}{25 m^{16} {(n^{5})}^{2}}$

Step 7.3

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

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Step 7.3.1

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

$\frac{9}{25 m^{16} n^{5 \cdot 2}}$

Step 7.3.2

Multiply $5$ by $2$ .

$\frac{9}{25 m^{16} n^{10}}$