Basic Math Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Multiply $5$ by $2$ .

$\frac{n^{10}}{{(m^{8})}^{2}}$

Step 4

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

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Step 4.1

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

$\frac{n^{10}}{m^{8 \cdot 2}}$

Step 4.2

Multiply $8$ by $2$ .

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