Basic Math Examples

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

Step 1

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

${(- 2 \frac{1}{m^{2}})}^{- 3}$

Step 2

Combine $- 2$ and $\frac{1}{m^{2}}$ .

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

Step 3

Move the negative in front of the fraction.

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

Step 4

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

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

Step 5

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

Tap for more steps...

Step 5.1

Apply the product rule to $- \frac{m^{2}}{2}$ .

${(- 1)}^{3} {(\frac{m^{2}}{2})}^{3}$

Step 5.2

Apply the product rule to $\frac{m^{2}}{2}$ .

${(- 1)}^{3} \frac{{(m^{2})}^{3}}{2^{3}}$

Step 6

Raise $- 1$ to the power of $3$ .

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

Step 7

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

Tap for more steps...

Step 7.1

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

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

Step 7.2

Multiply $2$ by $3$ .

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

Step 8

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

$- \frac{m^{6}}{8}$