Basic Math Examples

${(\frac{{pm}^{7}}{q^{3}})}^{3}$

Step 1

Rewrite the expression.

${(\frac{1}{q^{3}} {pm}^{7})}^{3}$

Step 2

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

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Step 2.1

Apply the product rule to $\frac{1}{q^{3}} {pm}^{7}$ .

${(\frac{1}{q^{3}})}^{3} {({pm}^{7})}^{3}$

Step 2.2

Apply the product rule to $\frac{1}{q^{3}}$ .

$\frac{1^{3}}{{(q^{3})}^{3}} {({pm}^{7})}^{3}$

Step 3

One to any power is one.

$\frac{1}{{(q^{3})}^{3}} {({pm}^{7})}^{3}$

Step 4

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

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Step 4.1

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

$\frac{1}{q^{3 \cdot 3}} {({pm}^{7})}^{3}$

Step 4.2

Multiply $3$ by $3$ .

$\frac{1}{q^{9}} {({pm}^{7})}^{3}$

Step 5

Multiply the exponents in ${({pm}^{7})}^{3}$ .

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Step 5.1

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

$\frac{1}{q^{9}} {pm}^{7 \cdot 3}$

Step 5.2

Multiply $7$ by $3$ .

$\frac{1}{q^{9}} {pm}^{21}$