Simplify (4x^2y^-2)/(2x^(1/2)y^2)

$\frac{4 x^{2} y^{- 2}}{2 x^{\frac{1}{2}} y^{2}}$

Move $y^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{4 x^{2}}{2 x^{\frac{1}{2}} y^{2} y^{2}}$

Multiply $y^{2}$ by $y^{2}$ by adding the exponents.

Move $y^{2}$ .

$\frac{4 x^{2}}{2 x^{\frac{1}{2}} (y^{2} y^{2})}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{4 x^{2}}{2 x^{\frac{1}{2}} y^{2 + 2}}$

Add $2$ and $2$ .

$\frac{4 x^{2}}{2 x^{\frac{1}{2}} y^{4}}$

Move $x^{\frac{1}{2}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$\frac{4 x^{2} x^{- \frac{1}{2}}}{2 y^{4}}$

Multiply $x^{2}$ by $x^{- \frac{1}{2}}$ by adding the exponents.

Move $x^{- \frac{1}{2}}$ .

$\frac{4 (x^{- \frac{1}{2}} x^{2})}{2 y^{4}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{4 x^{- \frac{1}{2} + 2}}{2 y^{4}}$

To write $2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{4 x^{- \frac{1}{2} + 2 \cdot \frac{2}{2}}}{2 y^{4}}$

Combine $2$ and $\frac{2}{2}$ .

$\frac{4 x^{- \frac{1}{2} + \frac{2 \cdot 2}{2}}}{2 y^{4}}$

Combine the numerators over the common denominator.

$\frac{4 x^{\frac{- 1 + 2 \cdot 2}{2}}}{2 y^{4}}$

Simplify the numerator.

Multiply $2$ by $2$ .

$\frac{4 x^{\frac{- 1 + 4}{2}}}{2 y^{4}}$

Add $- 1$ and $4$ .

$\frac{4 x^{\frac{3}{2}}}{2 y^{4}}$

Factor $2$ out of $4 x^{\frac{3}{2}}$ .

$\frac{2 (2 x^{\frac{3}{2}})}{2 y^{4}}$

Cancel the common factors.

Factor $2$ out of $2 y^{4}$ .

$\frac{2 (2 x^{\frac{3}{2}})}{2 (y^{4})}$

Cancel the common factor.

$\frac{2 (2 x^{\frac{3}{2}})}{2 y^{4}}$

Rewrite the expression.

$\frac{2 x^{\frac{3}{2}}}{y^{4}}$