Algebra Examples

${(\frac{2 x^{3}}{y})}^{3} \cdot \frac{1}{6 x^{3}}$

Step 1

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

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Step 1.1

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

$\frac{{(2 x^{3})}^{3}}{y^{3}} \cdot \frac{1}{6 x^{3}}$

Step 1.2

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

$\frac{2^{3} {(x^{3})}^{3}}{y^{3}} \cdot \frac{1}{6 x^{3}}$

Step 2

Combine fractions.

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Step 2.1

Combine.

$\frac{2^{3} {(x^{3})}^{3} \cdot 1}{y^{3} (6 x^{3})}$

Step 2.2

Multiply $2^{3}$ by $1$ .

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

Step 3

Simplify the numerator.

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Step 3.1

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

$\frac{8 {(x^{3})}^{3}}{y^{3} \cdot 6 x^{3}}$

Step 3.2

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

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Step 3.2.1

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

$\frac{8 x^{3 \cdot 3}}{y^{3} \cdot 6 x^{3}}$

Step 3.2.2

Multiply $3$ by $3$ .

$\frac{8 x^{9}}{y^{3} \cdot 6 x^{3}}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Cancel the common factor of $8$ and $6$ .

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Step 4.1.1

Factor $2$ out of $8 x^{9}$ .

$\frac{2 (4 x^{9})}{y^{3} \cdot 6 x^{3}}$

Step 4.1.2

Cancel the common factors.

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Step 4.1.2.1

Factor $2$ out of $y^{3} \cdot 6 x^{3}$ .

$\frac{2 (4 x^{9})}{2 (y^{3} \cdot 3 x^{3})}$

Step 4.1.2.2

Cancel the common factor.

$\frac{2 (4 x^{9})}{2 (y^{3} \cdot 3 x^{3})}$

Step 4.1.2.3

Rewrite the expression.

$\frac{4 x^{9}}{y^{3} \cdot 3 x^{3}}$

Step 4.2

Cancel the common factor of $x^{9}$ and $x^{3}$ .

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Step 4.2.1

Factor $x^{3}$ out of $4 x^{9}$ .

$\frac{x^{3} (4 x^{6})}{y^{3} \cdot 3 x^{3}}$

Step 4.2.2

Cancel the common factors.

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Step 4.2.2.1

Factor $x^{3}$ out of $y^{3} \cdot 3 x^{3}$ .

$\frac{x^{3} (4 x^{6})}{x^{3} (y^{3} \cdot 3)}$

Step 4.2.2.2

Cancel the common factor.

$\frac{x^{3} (4 x^{6})}{x^{3} (y^{3} \cdot 3)}$

Step 4.2.2.3

Rewrite the expression.

$\frac{4 x^{6}}{y^{3} \cdot 3}$

Step 4.3

Move $3$ to the left of $y^{3}$ .

$\frac{4 x^{6}}{3 y^{3}}$