Basic Math Examples

${(\frac{2 m^{3} n}{p^{2}})}^{3}$

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 $\frac{2 m^{3} n}{p^{2}}$ .

$\frac{{(2 m^{3} n)}^{3}}{{(p^{2})}^{3}}$

Step 1.2

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

$\frac{{(2 m^{3})}^{3} n^{3}}{{(p^{2})}^{3}}$

Step 1.3

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

$\frac{2^{3} {(m^{3})}^{3} n^{3}}{{(p^{2})}^{3}}$

Step 2

Simplify the numerator.

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Step 2.1

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

$\frac{8 {(m^{3})}^{3} n^{3}}{{(p^{2})}^{3}}$

Step 2.2

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

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Step 2.2.1

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

$\frac{8 m^{3 \cdot 3} n^{3}}{{(p^{2})}^{3}}$

Step 2.2.2

Multiply $3$ by $3$ .

$\frac{8 m^{9} n^{3}}{{(p^{2})}^{3}}$

Step 3

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

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Step 3.1

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

$\frac{8 m^{9} n^{3}}{p^{2 \cdot 3}}$

Step 3.2

Multiply $2$ by $3$ .

$\frac{8 m^{9} n^{3}}{p^{6}}$