Algebra Examples

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

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 $\frac{8 x y^{2}}{z^{3}}$ .

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

Step 1.2

Apply the product rule to $8 x y^{2}$ .

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

Step 1.3

Apply the product rule to $8 x$ .

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

Step 2

Simplify the numerator.

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Step 2.1

Raise $8$ to the power of $3$ .

$\frac{512 x^{3} {(y^{2})}^{3}}{{(z^{3})}^{3}}$

Step 2.2

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

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Step 2.2.1

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

$\frac{512 x^{3} y^{2 \cdot 3}}{{(z^{3})}^{3}}$

Step 2.2.2

Multiply $2$ by $3$ .

$\frac{512 x^{3} y^{6}}{{(z^{3})}^{3}}$

Step 3

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

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Step 3.1

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

$\frac{512 x^{3} y^{6}}{z^{3 \cdot 3}}$

Step 3.2

Multiply $3$ by $3$ .

$\frac{512 x^{3} y^{6}}{z^{9}}$