Algebra Examples

${(\frac{1}{4} a d^{3})}^{2}$

Step 1

Multiply $\frac{1}{4} (a d^{3})$ .

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Step 1.1

Combine $a$ and $\frac{1}{4}$ .

${(\frac{a}{4} d^{3})}^{2}$

Step 1.2

Combine $\frac{a}{4}$ and $d^{3}$ .

${(\frac{a d^{3}}{4})}^{2}$

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 $\frac{a d^{3}}{4}$ .

$\frac{{(a d^{3})}^{2}}{4^{2}}$

Step 2.2

Apply the product rule to $a d^{3}$ .

$\frac{a^{2} {(d^{3})}^{2}}{4^{2}}$

Step 3

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

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Step 3.1

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

$\frac{a^{2} d^{3 \cdot 2}}{4^{2}}$

Step 3.2

Multiply $3$ by $2$ .

$\frac{a^{2} d^{6}}{4^{2}}$

Step 4

Raise $4$ to the power of $2$ .

$\frac{a^{2} d^{6}}{16}$