Solve for x 3(x+5)^(1/3)-6=0

$3 {(x + 5)}^{\frac{1}{3}} - 6 = 0$

Step 1

Add $6$ to both sides of the equation.

$3 {(x + 5)}^{\frac{1}{3}} = 6$

Step 2

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

${(3 {(x + 5)}^{\frac{1}{3}})}^{3} = 6^{3}$

Step 3

Simplify the exponent.

Simplify the left side.

Simplify ${(3 {(x + 5)}^{\frac{1}{3}})}^{3}$ .

Apply the product rule to $3 {(x + 5)}^{\frac{1}{3}}$ .

$3^{3} {({(x + 5)}^{\frac{1}{3}})}^{3} = 6^{3}$

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

$27 {({(x + 5)}^{\frac{1}{3}})}^{3} = 6^{3}$

Multiply the exponents in ${({(x + 5)}^{\frac{1}{3}})}^{3}$ .

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

$27 {(x + 5)}^{\frac{1}{3} \cdot 3} = 6^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$27 {(x + 5)}^{\frac{1}{3} \cdot 3} = 6^{3}$

Rewrite the expression.

$27 {(x + 5)}^{1} = 6^{3}$

Simplify.

$27 (x + 5) = 6^{3}$

Apply the distributive property.

$27 x + 27 \cdot 5 = 6^{3}$

Multiply $27$ by $5$ .

$27 x + 135 = 6^{3}$

Simplify the right side.

Raise $6$ to the power of $3$ .

$27 x + 135 = 216$

Step 4

Solve for $x$ .

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

Subtract $135$ from both sides of the equation.

$27 x = 216 - 135$

Subtract $135$ from $216$ .

$27 x = 81$

Divide each term in $27 x = 81$ by $27$ and simplify.

Divide each term in $27 x = 81$ by $27$ .

$\frac{27 x}{27} = \frac{81}{27}$

Simplify the left side.

Cancel the common factor of $27$ .

Cancel the common factor.

$\frac{27 x}{27} = \frac{81}{27}$

Divide $x$ by $1$ .

$x = \frac{81}{27}$

Simplify the right side.

Divide $81$ by $27$ .

$x = 3$

Solve for x 3(x+5)^(1/3)-6=0

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