Precalculus Examples

${(125 x^{6})}^{\frac{2}{3}}$

Step 1

Simplify the expression.

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Step 1.1

Apply the product rule to $125 x^{6}$ .

$125^{\frac{2}{3}} {(x^{6})}^{\frac{2}{3}}$

Step 1.2

Rewrite $125$ as $5^{3}$ .

${(5^{3})}^{\frac{2}{3}} {(x^{6})}^{\frac{2}{3}}$

Step 1.3

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

$5^{3 (\frac{2}{3})} {(x^{6})}^{\frac{2}{3}}$

Step 2

Cancel the common factor of $3$ .

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Step 2.1

Cancel the common factor.

$5^{3 (\frac{2}{3})} {(x^{6})}^{\frac{2}{3}}$

Step 2.2

Rewrite the expression.

$5^{2} {(x^{6})}^{\frac{2}{3}}$

Step 3

Simplify the expression.

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Step 3.1

Raise $5$ to the power of $2$ .

$25 {(x^{6})}^{\frac{2}{3}}$

Step 3.2

Multiply the exponents in ${(x^{6})}^{\frac{2}{3}}$ .

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Step 3.2.1

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

$25 x^{6 (\frac{2}{3})}$

Step 3.2.2

Cancel the common factor of $3$ .

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Step 3.2.2.1

Factor $3$ out of $6$ .

$25 x^{3 (2) \frac{2}{3}}$

Step 3.2.2.2

Cancel the common factor.

$25 x^{3 \cdot 2 \frac{2}{3}}$

Step 3.2.2.3

Rewrite the expression.

$25 x^{2 \cdot 2}$

Step 3.2.3

Multiply $2$ by $2$ .

$25 x^{4}$