Algebra Examples

${(x - 2)}^{\frac{1}{3}} = 5$

Step 1

Raise each side of the equation to the power of $3$ to eliminate the fractional exponent on the left side.

${({(x - 2)}^{\frac{1}{3}})}^{3} = 5^{3}$

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 ${({(x - 2)}^{\frac{1}{3}})}^{3}$ .

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Step 2.1.1.1

Multiply the exponents in ${({(x - 2)}^{\frac{1}{3}})}^{3}$ .

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Step 2.1.1.1.1

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

${(x - 2)}^{\frac{1}{3} \cdot 3} = 5^{3}$

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.

${(x - 2)}^{\frac{1}{3} \cdot 3} = 5^{3}$

Step 2.1.1.1.2.2

Rewrite the expression.

${(x - 2)}^{1} = 5^{3}$

Step 2.1.1.2

Simplify.

$x - 2 = 5^{3}$

Step 2.2

Simplify the right side.

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Step 2.2.1

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

$x - 2 = 125$

Step 3

Move all terms not containing $x$ to the right side of the equation.

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Step 3.1

Add $2$ to both sides of the equation.

$x = 125 + 2$

Step 3.2

Add $125$ and $2$ .

$x = 127$