Algebra Examples

${(\frac{5 c d}{3 e f^{2}})}^{3}$

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 $\frac{5 c d}{3 e f^{2}}$ .

$\frac{{(5 c d)}^{3}}{{(3 e f^{2})}^{3}}$

Step 1.2

Apply the product rule to $5 c d$ .

$\frac{{(5 c)}^{3} d^{3}}{{(3 e f^{2})}^{3}}$

Step 1.3

Apply the product rule to $5 c$ .

$\frac{5^{3} c^{3} d^{3}}{{(3 e f^{2})}^{3}}$

Step 1.4

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

$\frac{5^{3} c^{3} d^{3}}{{(3 e)}^{3} {(f^{2})}^{3}}$

Step 1.5

Apply the product rule to $3 e$ .

$\frac{5^{3} c^{3} d^{3}}{3^{3} e^{3} {(f^{2})}^{3}}$

Step 2

Raise $5$ to the power of $3$ .

$\frac{125 c^{3} d^{3}}{3^{3} e^{3} {(f^{2})}^{3}}$

Step 3

Simplify the denominator.

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Step 3.1

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

$\frac{125 c^{3} d^{3}}{27 e^{3} {(f^{2})}^{3}}$

Step 3.2

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

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Step 3.2.1

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

$\frac{125 c^{3} d^{3}}{27 e^{3} f^{2 \cdot 3}}$

Step 3.2.2

Multiply $2$ by $3$ .

$\frac{125 c^{3} d^{3}}{27 e^{3} f^{6}}$