Algebra Examples

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

Step 1

Cancel the common factor of $4$ and $2$ .

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Step 1.1

Factor $2$ out of $4$ .

${(\frac{2 \cdot 2}{2 d^{2}})}^{3}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $2 d^{2}$ .

${(\frac{2 \cdot 2}{2 (d^{2})})}^{3}$

Step 1.2.2

Cancel the common factor.

${(\frac{2 \cdot 2}{2 d^{2}})}^{3}$

Step 1.2.3

Rewrite the expression.

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

Step 2

Simplify the expression.

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Step 2.1

Apply the product rule to $\frac{2}{d^{2}}$ .

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

Step 2.2

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

$\frac{8}{{(d^{2})}^{3}}$

Step 2.3

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

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Step 2.3.1

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

$\frac{8}{d^{2 \cdot 3}}$

Step 2.3.2

Multiply $2$ by $3$ .

$\frac{8}{d^{6}}$