Simplify (2m^2)^-1(4m^(3/2))

${(2 m^{2})}^{- 1} (4 m^{\frac{3}{2}})$

Rewrite using the commutative property of multiplication.

$4 {(2 m^{2})}^{- 1} m^{\frac{3}{2}}$

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

$4 \frac{1}{2 m^{2}} m^{\frac{3}{2}}$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

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

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

Factor $m^{\frac{3}{2}}$ out of $m^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{2}{m^{\frac{1}{2}}}$