Precalculus Examples

$x^{\frac{3}{4}} = 125$

Step 1

Raise each side of the equation to the power of $\frac{4}{3}$ to eliminate the fractional exponent on the left side.

${(x^{\frac{3}{4}})}^{\frac{4}{3}} = 125^{\frac{4}{3}}$

Step 2

Simplify the exponent.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify ${(x^{\frac{3}{4}})}^{\frac{4}{3}}$ .

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Step 2.1.1.1

Multiply the exponents in ${(x^{\frac{3}{4}})}^{\frac{4}{3}}$ .

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Step 2.1.1.1.1

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

$x^{\frac{3}{4} \cdot \frac{4}{3}} = 125^{\frac{4}{3}}$

Step 2.1.1.1.2

Cancel the common factor of $3$ .

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Step 2.1.1.1.2.1

Cancel the common factor.

$x^{\frac{3}{4} \cdot \frac{4}{3}} = 125^{\frac{4}{3}}$

Step 2.1.1.1.2.2

Rewrite the expression.

$x^{\frac{1}{4} \cdot 4} = 125^{\frac{4}{3}}$

Step 2.1.1.1.3

Cancel the common factor of $4$ .

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Step 2.1.1.1.3.1

Cancel the common factor.

$x^{\frac{1}{4} \cdot 4} = 125^{\frac{4}{3}}$

Step 2.1.1.1.3.2

Rewrite the expression.

$x^{1} = 125^{\frac{4}{3}}$

Step 2.1.1.2

Simplify.

$x = 125^{\frac{4}{3}}$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $125^{\frac{4}{3}}$ .

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Step 2.2.1.1

Simplify the expression.

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Step 2.2.1.1.1

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

$x = {(5^{3})}^{\frac{4}{3}}$

Step 2.2.1.1.2

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

$x = 5^{3 (\frac{4}{3})}$

Step 2.2.1.2

Cancel the common factor of $3$ .

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Step 2.2.1.2.1

Cancel the common factor.

$x = 5^{3 (\frac{4}{3})}$

Step 2.2.1.2.2

Rewrite the expression.

$x = 5^{4}$

Step 2.2.1.3

Raise $5$ to the power of $4$ .

$x = 625$