Simplify (10m^3)^-2

${(10 m^{3})}^{- 2}$

Step 1

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

$\frac{1}{{(10 m^{3})}^{2}}$

Step 2

Simplify the denominator.

Apply the product rule to $10 m^{3}$ .

$\frac{1}{10^{2} {(m^{3})}^{2}}$

Raise $10$ to the power of $2$ .

$\frac{1}{100 {(m^{3})}^{2}}$

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

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

$\frac{1}{100 m^{3 \cdot 2}}$

Multiply $3$ by $2$ .

$\frac{1}{100 m^{6}}$