Algebra Examples

${(\frac{x^{0} y^{- 3} z^{2}}{2 x^{3} y^{2} z^{- 4}})}^{3}$

Step 1

Move $x^{0}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{y^{- 3} z^{2}}{2 x^{3} y^{2} z^{- 4} x^{0}})}^{3}$

Step 2

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

${(\frac{z^{2}}{2 x^{3} y^{2} z^{- 4} x^{0} y^{3}})}^{3}$

Step 3

Simplify the denominator.

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Step 3.1

Multiply $x^{3}$ by $x^{0}$ by adding the exponents.

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Step 3.1.1

Move $x^{0}$ .

${(\frac{z^{2}}{2 (x^{0} x^{3}) y^{2} z^{- 4} y^{3}})}^{3}$

Step 3.1.2

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

${(\frac{z^{2}}{2 x^{0 + 3} y^{2} z^{- 4} y^{3}})}^{3}$

Step 3.1.3

Add $0$ and $3$ .

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

Step 3.2

Multiply $y^{2}$ by $y^{3}$ by adding the exponents.

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Step 3.2.1

Move $y^{3}$ .

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

Step 3.2.2

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

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

Step 3.2.3

Add $3$ and $2$ .

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

Step 4

Move $z^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 5

Multiply $z^{2}$ by $z^{4}$ by adding the exponents.

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Step 5.1

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

${(\frac{z^{2 + 4}}{2 x^{3} y^{5}})}^{3}$

Step 5.2

Add $2$ and $4$ .

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

Step 6

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

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Step 6.1

Apply the product rule to $\frac{z^{6}}{2 x^{3} y^{5}}$ .

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

Step 6.2

Apply the product rule to $2 x^{3} y^{5}$ .

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

Step 6.3

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

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

Step 7

Multiply the exponents in ${(z^{6})}^{3}$ .

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Step 7.1

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

$\frac{z^{6 \cdot 3}}{2^{3} {(x^{3})}^{3} {(y^{5})}^{3}}$

Step 7.2

Multiply $6$ by $3$ .

$\frac{z^{18}}{2^{3} {(x^{3})}^{3} {(y^{5})}^{3}}$

Step 8

Simplify the denominator.

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Step 8.1

Raise $2$ to the power of $3$ .

$\frac{z^{18}}{8 {(x^{3})}^{3} {(y^{5})}^{3}}$

Step 8.2

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

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Step 8.2.1

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

$\frac{z^{18}}{8 x^{3 \cdot 3} {(y^{5})}^{3}}$

Step 8.2.2

Multiply $3$ by $3$ .

$\frac{z^{18}}{8 x^{9} {(y^{5})}^{3}}$

Step 8.3

Multiply the exponents in ${(y^{5})}^{3}$ .

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Step 8.3.1

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

$\frac{z^{18}}{8 x^{9} y^{5 \cdot 3}}$

Step 8.3.2

Multiply $5$ by $3$ .

$\frac{z^{18}}{8 x^{9} y^{15}}$