Algebra Examples

${(\frac{- 2 x y^{- 3}}{3 x^{- 1}})}^{4} \cdot {(w^{2} y)}^{- 2}$

Step 1

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

${(\frac{- 2 x}{3 x^{- 1} y^{3}})}^{4} \cdot {(w^{2} y)}^{- 2}$

Step 2

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

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

Step 3

Multiply $x$ by $x$ by adding the exponents.

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Step 3.1

Move $x$ .

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

Step 3.2

Multiply $x$ by $x$ .

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

Step 4

Move the negative in front of the fraction.

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

Step 5

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 5.1

Apply the product rule to $- \frac{2 x^{2}}{3 y^{3}}$ .

${(- 1)}^{4} {(\frac{2 x^{2}}{3 y^{3}})}^{4} \cdot {(w^{2} y)}^{- 2}$

Step 5.2

Apply the product rule to $\frac{2 x^{2}}{3 y^{3}}$ .

${(- 1)}^{4} \frac{{(2 x^{2})}^{4}}{{(3 y^{3})}^{4}} \cdot {(w^{2} y)}^{- 2}$

Step 5.3

Apply the product rule to $2 x^{2}$ .

${(- 1)}^{4} \frac{2^{4} {(x^{2})}^{4}}{{(3 y^{3})}^{4}} \cdot {(w^{2} y)}^{- 2}$

Step 5.4

Apply the product rule to $3 y^{3}$ .

${(- 1)}^{4} \frac{2^{4} {(x^{2})}^{4}}{3^{4} {(y^{3})}^{4}} \cdot {(w^{2} y)}^{- 2}$

Step 6

Simplify the expression.

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Step 6.1

Raise $- 1$ to the power of $4$ .

$1 \frac{2^{4} {(x^{2})}^{4}}{3^{4} {(y^{3})}^{4}} \cdot {(w^{2} y)}^{- 2}$

Step 6.2

Multiply $\frac{2^{4} {(x^{2})}^{4}}{3^{4} {(y^{3})}^{4}}$ by $1$ .

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

Step 7

Simplify the numerator.

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Step 7.1

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

$\frac{16 {(x^{2})}^{4}}{3^{4} {(y^{3})}^{4}} \cdot {(w^{2} y)}^{- 2}$

Step 7.2

Multiply the exponents in ${(x^{2})}^{4}$ .

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Step 7.2.1

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

$\frac{16 x^{2 \cdot 4}}{3^{4} {(y^{3})}^{4}} \cdot {(w^{2} y)}^{- 2}$

Step 7.2.2

Multiply $2$ by $4$ .

$\frac{16 x^{8}}{3^{4} {(y^{3})}^{4}} \cdot {(w^{2} y)}^{- 2}$

Step 8

Simplify the denominator.

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Step 8.1

Raise $3$ to the power of $4$ .

$\frac{16 x^{8}}{81 {(y^{3})}^{4}} \cdot {(w^{2} y)}^{- 2}$

Step 8.2

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

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Step 8.2.1

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

$\frac{16 x^{8}}{81 y^{3 \cdot 4}} \cdot {(w^{2} y)}^{- 2}$

Step 8.2.2

Multiply $3$ by $4$ .

$\frac{16 x^{8}}{81 y^{12}} \cdot {(w^{2} y)}^{- 2}$

Step 9

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

$\frac{16 x^{8}}{81 y^{12}} \cdot \frac{1}{{(w^{2} y)}^{2}}$

Step 10

Combine fractions.

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Step 10.1

Combine.

$\frac{16 x^{8} \cdot 1}{81 y^{12} {(w^{2} y)}^{2}}$

Step 10.2

Multiply $16$ by $1$ .

$\frac{16 x^{8}}{81 y^{12} {(w^{2} y)}^{2}}$

Step 11

Simplify the denominator.

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Step 11.1

Apply the product rule to $w^{2} y$ .

$\frac{16 x^{8}}{81 y^{12} {(w^{2})}^{2} y^{2}}$

Step 11.2

Multiply $y^{12}$ by $y^{2}$ by adding the exponents.

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Step 11.2.1

Move $y^{2}$ .

$\frac{16 x^{8}}{81 (y^{2} y^{12}) {(w^{2})}^{2}}$

Step 11.2.2

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

$\frac{16 x^{8}}{81 y^{2 + 12} {(w^{2})}^{2}}$

Step 11.2.3

Add $2$ and $12$ .

$\frac{16 x^{8}}{81 y^{14} {(w^{2})}^{2}}$

Step 11.3

Multiply the exponents in ${(w^{2})}^{2}$ .

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Step 11.3.1

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

$\frac{16 x^{8}}{81 y^{14} w^{2 \cdot 2}}$

Step 11.3.2

Multiply $2$ by $2$ .

$\frac{16 x^{8}}{81 y^{14} w^{4}}$