Algebra Examples

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

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

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

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

Step 1.2

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

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Step 1.2.1

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

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

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

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

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

Step 1.2.2.2

Cancel the common factor.

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

Step 1.2.2.3

Rewrite the expression.

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

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $2 x$ .

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

Step 2.2

Combine exponents.

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Step 2.2.1

Factor out negative.

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

Step 2.2.2

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

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

Step 2.2.3

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

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

Step 2.2.4

Add $2$ and $2$ .

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

Step 2.2.5

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

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Step 2.2.5.1

Move $x^{2}$ .

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

Step 2.2.5.2

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

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

Step 2.2.5.3

Add $2$ and $2$ .

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

Step 2.3

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

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

Step 2.4

Combine exponents.

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Step 2.4.1

Factor out negative.

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

Step 2.4.2

Multiply $16$ by $- 1$ .

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

Step 3

Move the negative in front of the fraction.

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