Algebra Examples

${(9 - x)}^{\frac{1}{3}} + 12 = 15$

Step 1

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

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Step 1.1

Subtract $12$ from both sides of the equation.

${(9 - x)}^{\frac{1}{3}} = 15 - 12$

Step 1.2

Subtract $12$ from $15$ .

${(9 - x)}^{\frac{1}{3}} = 3$

Step 2

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

${({(9 - x)}^{\frac{1}{3}})}^{3} = 3^{3}$

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 ${({(9 - x)}^{\frac{1}{3}})}^{3}$ .

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Step 3.1.1.1

Multiply the exponents in ${({(9 - x)}^{\frac{1}{3}})}^{3}$ .

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Step 3.1.1.1.1

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

${(9 - x)}^{\frac{1}{3} \cdot 3} = 3^{3}$

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.

${(9 - x)}^{\frac{1}{3} \cdot 3} = 3^{3}$

Step 3.1.1.1.2.2

Rewrite the expression.

${(9 - x)}^{1} = 3^{3}$

Step 3.1.1.2

Simplify.

$9 - x = 3^{3}$

Step 3.2

Simplify the right side.

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Step 3.2.1

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

$9 - x = 27$

Step 4

Solve for $x$ .

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Step 4.1

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

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Step 4.1.1

Subtract $9$ from both sides of the equation.

$- x = 27 - 9$

Step 4.1.2

Subtract $9$ from $27$ .

$- x = 18$

Step 4.2

Divide each term in $- x = 18$ by $- 1$ and simplify.

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Step 4.2.1

Divide each term in $- x = 18$ by $- 1$ .

$\frac{- x}{- 1} = \frac{18}{- 1}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{18}{- 1}$

Step 4.2.2.2

Divide $x$ by $1$ .

$x = \frac{18}{- 1}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $18$ by $- 1$ .

$x = - 18$