Basic Math Examples

${(m^{6})}^{- \frac{2}{3}}$

Step 1

Multiply the exponents in ${(m^{6})}^{- \frac{2}{3}}$ .

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Step 1.1

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

$m^{6 (- \frac{2}{3})}$

Step 1.2

Cancel the common factor of $3$ .

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Step 1.2.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$m^{6 (\frac{- 2}{3})}$

Step 1.2.2

Factor $3$ out of $6$ .

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

Step 1.2.3

Cancel the common factor.

$m^{3 \cdot 2 \frac{- 2}{3}}$

Step 1.2.4

Rewrite the expression.

$m^{2 \cdot - 2}$

Step 1.3

Multiply $2$ by $- 2$ .

$m^{- 4}$

Step 2

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

$\frac{1}{m^{4}}$