Algebra Examples

${(x - 1)}^{\frac{1}{3}} - 4 = - 4$

Step 1

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

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Step 1.1

Add $4$ to both sides of the equation.

${(x - 1)}^{\frac{1}{3}} = - 4 + 4$

Step 1.2

Add $- 4$ and $4$ .

${(x - 1)}^{\frac{1}{3}} = 0$

Step 2

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

${({(x - 1)}^{\frac{1}{3}})}^{3} = 0^{3}$

Step 3

Simplify the exponent.

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Step 3.1

Simplify the left side.

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Step 3.1.1

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

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Step 3.1.1.1

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

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Step 3.1.1.1.1

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

${(x - 1)}^{\frac{1}{3} \cdot 3} = 0^{3}$

Step 3.1.1.1.2

Cancel the common factor of $3$ .

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Step 3.1.1.1.2.1

Cancel the common factor.

${(x - 1)}^{\frac{1}{3} \cdot 3} = 0^{3}$

Step 3.1.1.1.2.2

Rewrite the expression.

${(x - 1)}^{1} = 0^{3}$

Step 3.1.1.2

Simplify.

$x - 1 = 0^{3}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Raising $0$ to any positive power yields $0$ .

$x - 1 = 0$

Step 4

Add $1$ to both sides of the equation.

$x = 1$