Basic Math Examples

${(\frac{2 y \cdot 3}{8})}^{3}$

Step 1

Cancel the common factor of $2$ and $8$ .

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Step 1.1

Factor $2$ out of $2 y \cdot 3$ .

${(\frac{2 (y \cdot 3)}{8})}^{3}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $8$ .

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

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

Step 2

Move $3$ to the left of $y$ .

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

Step 3

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

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Step 3.1

Apply the product rule to $\frac{3 y}{4}$ .

$\frac{{(3 y)}^{3}}{4^{3}}$

Step 3.2

Apply the product rule to $3 y$ .

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

Step 4

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

$\frac{27 y^{3}}{4^{3}}$

Step 5

Raise $4$ to the power of $3$ .

$\frac{27 y^{3}}{64}$