Simplify (m^-3t^-3)/((m^2t^3)^-1)

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

Step 1

Simplify the expression.

Move $m^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Move $t^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Move ${(m^{2} t^{3})}^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{m^{2} t^{3}}{m^{3} t^{3}}$

Step 2

Cancel the common factor of $m^{2}$ and $m^{3}$ .

Factor $m^{2}$ out of $m^{2} t^{3}$ .

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

Cancel the common factors.

Factor $m^{2}$ out of $m^{3} t^{3}$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{t^{3}}{m t^{3}}$

Step 3

Cancel the common factor of $t^{3}$ .

Cancel the common factor.

$\frac{t^{3}}{m t^{3}}$

Rewrite the expression.

$\frac{1}{m}$