Algebra Examples

$- \frac{2 {(p^{- 4} y^{4})}^{- 3}}{6 p^{- 3} y^{- 1}}$

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

Move ${(p^{- 4} y^{4})}^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$- \frac{2}{6 p^{- 3} y^{- 1} {(p^{- 4} y^{4})}^{3}}$

Step 1.2

Simplify the expression.

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Step 1.2.1

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

$- \frac{2 p^{3}}{6 y^{- 1} {(p^{- 4} y^{4})}^{3}}$

Step 1.2.2

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

$- \frac{2 p^{3} y}{6 {(p^{- 4} y^{4})}^{3}}$

Step 1.3

Cancel the common factor of $2$ and $6$ .

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Step 1.3.1

Factor $2$ out of $2 p^{3} y$ .

$- \frac{2 (p^{3} y)}{6 {(p^{- 4} y^{4})}^{3}}$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $2$ out of $6 {(p^{- 4} y^{4})}^{3}$ .

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

Step 1.3.2.2

Cancel the common factor.

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

Step 1.3.2.3

Rewrite the expression.

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

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $p^{- 4} y^{4}$ .

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

Step 2.2

Multiply the exponents in ${(p^{- 4})}^{3}$ .

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Step 2.2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 2.2.2

Multiply $- 4$ by $3$ .

$- \frac{p^{3} y}{3 p^{- 12} {(y^{4})}^{3}}$

Step 2.3

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

$- \frac{p^{3} y}{3 \frac{1}{p^{12}} {(y^{4})}^{3}}$

Step 2.4

Multiply the exponents in ${(y^{4})}^{3}$ .

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Step 2.4.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- \frac{p^{3} y}{3 \frac{1}{p^{12}} y^{4 \cdot 3}}$

Step 2.4.2

Multiply $4$ by $3$ .

$- \frac{p^{3} y}{3 \frac{1}{p^{12}} y^{12}}$

Step 2.5

Combine exponents.

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Step 2.5.1

Combine $3$ and $\frac{1}{p^{12}}$ .

$- \frac{p^{3} y}{\frac{3}{p^{12}} y^{12}}$

Step 2.5.2

Combine $\frac{3}{p^{12}}$ and $y^{12}$ .

$- \frac{p^{3} y}{\frac{3 y^{12}}{p^{12}}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$- (p^{3} y \frac{p^{12}}{3 y^{12}})$

Step 4

Cancel the common factor of $y$ .

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Step 4.1

Factor $y$ out of $p^{3} y$ .

$- (y p^{3} \frac{p^{12}}{3 y^{12}})$

Step 4.2

Factor $y$ out of $3 y^{12}$ .

$- (y p^{3} \frac{p^{12}}{y (3 y^{11})})$

Step 4.3

Cancel the common factor.

$- (y p^{3} \frac{p^{12}}{y (3 y^{11})})$

Step 4.4

Rewrite the expression.

$- (p^{3} \frac{p^{12}}{3 y^{11}})$

Step 5

Combine $p^{3}$ and $\frac{p^{12}}{3 y^{11}}$ .

$- \frac{p^{3} p^{12}}{3 y^{11}}$

Step 6

Multiply $p^{3}$ by $p^{12}$ by adding the exponents.

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Step 6.1

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

$- \frac{p^{3 + 12}}{3 y^{11}}$

Step 6.2

Add $3$ and $12$ .

$- \frac{p^{15}}{3 y^{11}}$