Simplify ((2x)^-2y^5)/(-4x^2y^2)

$\frac{{(2 x)}^{- 2} y^{5}}{- 4 x^{2} y^{2}}$

Step 1

Reduce the expression by cancelling the common factors.

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

$\frac{y^{5}}{- 4 x^{2} y^{2} {(2 x)}^{2}}$

Cancel the common factor of $y^{5}$ and $y^{2}$ .

Factor $y^{2}$ out of $y^{5}$ .

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

Cancel the common factors.

Factor $y^{2}$ out of $- 4 x^{2} y^{2} {(2 x)}^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

Simplify the denominator.

Apply the product rule to $2 x$ .

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

Combine exponents.

Factor out negative.

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

Rewrite $4$ as $2^{2}$ .

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

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

$\frac{y^{3}}{x^{2} \cdot (- 2^{2 + 2}) x^{2}}$

Add $2$ and $2$ .

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

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

Move $x^{2}$ .

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

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

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

Add $2$ and $2$ .

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

Raise $2$ to the power of $4$ .

$\frac{y^{3}}{x^{4} \cdot - 1 \cdot 16}$

Combine exponents.

Factor out negative.

$\frac{y^{3}}{- (x^{4} \cdot 16)}$

Multiply $16$ by $- 1$ .

$\frac{y^{3}}{- 16 x^{4}}$

Step 3

Move the negative in front of the fraction.

$- \frac{y^{3}}{16 x^{4}}$