Algebra Examples

${(- 2 x^{- 4} y^{7} z^{- 8})}^{- 4}$

Step 1

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

${(- 2 \frac{1}{x^{4}} y^{7} z^{- 8})}^{- 4}$

Step 2

Combine $- 2$ and $\frac{1}{x^{4}}$ .

${(\frac{- 2}{x^{4}} y^{7} z^{- 8})}^{- 4}$

Step 3

Move the negative in front of the fraction.

${(- \frac{2}{x^{4}} y^{7} z^{- 8})}^{- 4}$

Step 4

Combine $y^{7}$ and $\frac{2}{x^{4}}$ .

${(- \frac{y^{7} \cdot 2}{x^{4}} z^{- 8})}^{- 4}$

Step 5

Move $2$ to the left of $y^{7}$ .

${(- \frac{2 \cdot y^{7}}{x^{4}} z^{- 8})}^{- 4}$

Step 6

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

${(- \frac{2 y^{7}}{x^{4}} \cdot \frac{1}{z^{8}})}^{- 4}$

Step 7

Multiply $\frac{1}{z^{8}}$ by $\frac{2 y^{7}}{x^{4}}$ .

${(- \frac{2 y^{7}}{z^{8} x^{4}})}^{- 4}$

Step 8

Change the sign of the exponent by rewriting the base as its reciprocal.

${(- \frac{z^{8} x^{4}}{2 y^{7}})}^{4}$

Step 9

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

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Step 9.1

Apply the product rule to $- \frac{z^{8} x^{4}}{2 y^{7}}$ .

${(- 1)}^{4} {(\frac{z^{8} x^{4}}{2 y^{7}})}^{4}$

Step 9.2

Apply the product rule to $\frac{z^{8} x^{4}}{2 y^{7}}$ .

${(- 1)}^{4} \frac{{(z^{8} x^{4})}^{4}}{{(2 y^{7})}^{4}}$

Step 9.3

Apply the product rule to $z^{8} x^{4}$ .

${(- 1)}^{4} \frac{{(z^{8})}^{4} {(x^{4})}^{4}}{{(2 y^{7})}^{4}}$

Step 9.4

Apply the product rule to $2 y^{7}$ .

${(- 1)}^{4} \frac{{(z^{8})}^{4} {(x^{4})}^{4}}{2^{4} {(y^{7})}^{4}}$

Step 10

Simplify the expression.

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Step 10.1

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

$1 \frac{{(z^{8})}^{4} {(x^{4})}^{4}}{2^{4} {(y^{7})}^{4}}$

Step 10.2

Multiply $\frac{{(z^{8})}^{4} {(x^{4})}^{4}}{2^{4} {(y^{7})}^{4}}$ by $1$ .

$\frac{{(z^{8})}^{4} {(x^{4})}^{4}}{2^{4} {(y^{7})}^{4}}$

Step 11

Simplify the numerator.

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Step 11.1

Multiply the exponents in ${(z^{8})}^{4}$ .

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Step 11.1.1

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

$\frac{z^{8 \cdot 4} {(x^{4})}^{4}}{2^{4} {(y^{7})}^{4}}$

Step 11.1.2

Multiply $8$ by $4$ .

$\frac{z^{32} {(x^{4})}^{4}}{2^{4} {(y^{7})}^{4}}$

Step 11.2

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

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Step 11.2.1

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

$\frac{z^{32} x^{4 \cdot 4}}{2^{4} {(y^{7})}^{4}}$

Step 11.2.2

Multiply $4$ by $4$ .

$\frac{z^{32} x^{16}}{2^{4} {(y^{7})}^{4}}$

Step 12

Simplify the denominator.

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Step 12.1

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

$\frac{z^{32} x^{16}}{16 {(y^{7})}^{4}}$

Step 12.2

Multiply the exponents in ${(y^{7})}^{4}$ .

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Step 12.2.1

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

$\frac{z^{32} x^{16}}{16 y^{7 \cdot 4}}$

Step 12.2.2

Multiply $7$ by $4$ .

$\frac{z^{32} x^{16}}{16 y^{28}}$