Algebra Examples

${(\frac{z^{2} y^{- 1} x^{- 3}}{x^{- 8} z^{6} y^{4}})}^{- 4}$

Step 1

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

${(\frac{z^{2} x^{- 3}}{x^{- 8} z^{6} y^{4} y})}^{- 4}$

Step 2

Multiply $y^{4}$ by $y$ by adding the exponents.

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Step 2.1

Move $y$ .

${(\frac{z^{2} x^{- 3}}{x^{- 8} z^{6} (y \cdot y^{4})})}^{- 4}$

Step 2.2

Multiply $y$ by $y^{4}$ .

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Step 2.2.1

Raise $y$ to the power of $1$ .

${(\frac{z^{2} x^{- 3}}{x^{- 8} z^{6} (y^{1} y^{4})})}^{- 4}$

Step 2.2.2

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

${(\frac{z^{2} x^{- 3}}{x^{- 8} z^{6} y^{1 + 4}})}^{- 4}$

Step 2.3

Add $1$ and $4$ .

${(\frac{z^{2} x^{- 3}}{x^{- 8} z^{6} y^{5}})}^{- 4}$

Step 3

Move $x^{- 8}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(\frac{z^{2} x^{- 3} x^{8}}{z^{6} y^{5}})}^{- 4}$

Step 4

Multiply $x^{- 3}$ by $x^{8}$ by adding the exponents.

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Step 4.1

Move $x^{8}$ .

${(\frac{z^{2} (x^{8} x^{- 3})}{z^{6} y^{5}})}^{- 4}$

Step 4.2

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

${(\frac{z^{2} x^{8 - 3}}{z^{6} y^{5}})}^{- 4}$

Step 4.3

Subtract $3$ from $8$ .

${(\frac{z^{2} x^{5}}{z^{6} y^{5}})}^{- 4}$

Step 5

Cancel the common factor of $z^{2}$ and $z^{6}$ .

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Step 5.1

Factor $z^{2}$ out of $z^{2} x^{5}$ .

${(\frac{z^{2} (x^{5})}{z^{6} y^{5}})}^{- 4}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $z^{2}$ out of $z^{6} y^{5}$ .

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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

Step 6

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

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

Step 7

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

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Step 7.1

Apply the product rule to $\frac{z^{4} y^{5}}{x^{5}}$ .

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

Step 7.2

Apply the product rule to $z^{4} y^{5}$ .

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

Step 8

Simplify the numerator.

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Step 8.1

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

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Step 8.1.1

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

$\frac{z^{4 \cdot 4} {(y^{5})}^{4}}{{(x^{5})}^{4}}$

Step 8.1.2

Multiply $4$ by $4$ .

$\frac{z^{16} {(y^{5})}^{4}}{{(x^{5})}^{4}}$

Step 8.2

Multiply the exponents in ${(y^{5})}^{4}$ .

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Step 8.2.1

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

$\frac{z^{16} y^{5 \cdot 4}}{{(x^{5})}^{4}}$

Step 8.2.2

Multiply $5$ by $4$ .

$\frac{z^{16} y^{20}}{{(x^{5})}^{4}}$

Step 9

Multiply the exponents in ${(x^{5})}^{4}$ .

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Step 9.1

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

$\frac{z^{16} y^{20}}{x^{5 \cdot 4}}$

Step 9.2

Multiply $5$ by $4$ .

$\frac{z^{16} y^{20}}{x^{20}}$