Algebra Examples

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

Step 1

Multiply $x^{3}$ by $x^{- 4}$ by adding the exponents.

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Step 1.1

Move $x^{- 4}$ .

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

Step 1.2

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

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

Step 1.3

Add $- 4$ and $3$ .

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

Step 2

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

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Step 2.1

Move $z^{3}$ .

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

Step 2.2

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

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

Step 2.3

Add $3$ and $2$ .

$\frac{{(2 x^{3} z^{2})}^{3}}{x^{- 1} y^{4} z^{5}}$

Step 3

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

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

Step 4

Simplify the numerator.

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Step 4.1

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

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

Step 4.2

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

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

Step 4.3

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

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

Step 4.4

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

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Step 4.4.1

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

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

Step 4.4.2

Multiply $3$ by $3$ .

$\frac{8 x^{9} {(z^{2})}^{3} x}{y^{4} z^{5}}$

Step 4.5

Multiply the exponents in ${(z^{2})}^{3}$ .

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Step 4.5.1

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

$\frac{8 x^{9} z^{2 \cdot 3} x}{y^{4} z^{5}}$

Step 4.5.2

Multiply $2$ by $3$ .

$\frac{8 x^{9} z^{6} x}{y^{4} z^{5}}$

Step 4.6

Combine exponents.

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Step 4.6.1

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

$\frac{8 (x^{1} x^{9}) z^{6}}{y^{4} z^{5}}$

Step 4.6.2

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

$\frac{8 x^{1 + 9} z^{6}}{y^{4} z^{5}}$

Step 4.6.3

Add $1$ and $9$ .

$\frac{8 x^{10} z^{6}}{y^{4} z^{5}}$

Step 5

Cancel the common factor of $z^{6}$ and $z^{5}$ .

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Step 5.1

Factor $z^{5}$ out of $8 x^{10} z^{6}$ .

$\frac{z^{5} (8 x^{10} z)}{y^{4} z^{5}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $z^{5}$ out of $y^{4} z^{5}$ .

$\frac{z^{5} (8 x^{10} z)}{z^{5} y^{4}}$

Step 5.2.2

Cancel the common factor.

$\frac{z^{5} (8 x^{10} z)}{z^{5} y^{4}}$

Step 5.2.3

Rewrite the expression.

$\frac{8 x^{10} z}{y^{4}}$