Algebra Examples

${(\frac{p^{2} t^{7}}{10})}^{3}$

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 $\frac{p^{2} t^{7}}{10}$ .

$\frac{{(p^{2} t^{7})}^{3}}{10^{3}}$

Step 1.2

Apply the product rule to $p^{2} t^{7}$ .

$\frac{{(p^{2})}^{3} {(t^{7})}^{3}}{10^{3}}$

Step 2

Simplify the numerator.

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Step 2.1

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

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Step 2.1.1

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

$\frac{p^{2 \cdot 3} {(t^{7})}^{3}}{10^{3}}$

Step 2.1.2

Multiply $2$ by $3$ .

$\frac{p^{6} {(t^{7})}^{3}}{10^{3}}$

Step 2.2

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

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Step 2.2.1

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

$\frac{p^{6} t^{7 \cdot 3}}{10^{3}}$

Step 2.2.2

Multiply $7$ by $3$ .

$\frac{p^{6} t^{21}}{10^{3}}$

Step 3

Raise $10$ to the power of $3$ .

$\frac{p^{6} t^{21}}{1000}$