Basic Math Examples

${(\frac{4 p^{8} q}{3 r^{3}})}^{3}$

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 $\frac{4 p^{8} q}{3 r^{3}}$ .

$\frac{{(4 p^{8} q)}^{3}}{{(3 r^{3})}^{3}}$

Step 1.2

Apply the product rule to $4 p^{8} q$ .

$\frac{{(4 p^{8})}^{3} q^{3}}{{(3 r^{3})}^{3}}$

Step 1.3

Apply the product rule to $4 p^{8}$ .

$\frac{4^{3} {(p^{8})}^{3} q^{3}}{{(3 r^{3})}^{3}}$

Step 1.4

Apply the product rule to $3 r^{3}$ .

$\frac{4^{3} {(p^{8})}^{3} q^{3}}{3^{3} {(r^{3})}^{3}}$

Step 2

Simplify the numerator.

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Step 2.1

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

$\frac{64 {(p^{8})}^{3} q^{3}}{3^{3} {(r^{3})}^{3}}$

Step 2.2

Multiply the exponents in ${(p^{8})}^{3}$ .

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Step 2.2.1

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

$\frac{64 p^{8 \cdot 3} q^{3}}{3^{3} {(r^{3})}^{3}}$

Step 2.2.2

Multiply $8$ by $3$ .

$\frac{64 p^{24} q^{3}}{3^{3} {(r^{3})}^{3}}$

Step 3

Simplify the denominator.

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Step 3.1

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

$\frac{64 p^{24} q^{3}}{27 {(r^{3})}^{3}}$

Step 3.2

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

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Step 3.2.1

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

$\frac{64 p^{24} q^{3}}{27 r^{3 \cdot 3}}$

Step 3.2.2

Multiply $3$ by $3$ .

$\frac{64 p^{24} q^{3}}{27 r^{9}}$