Solve for x fifth root of 27(x-2)=3

$\sqrt[5]{27 (x - 2)} = 3$

Step 1

To remove the radical on the left side of the equation, raise both sides of the equation to the power of $5$ .

${\sqrt[5]{27 (x - 2)}}^{5} = 3^{5}$

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{27 (x - 2)}$ as ${(27 (x - 2))}^{\frac{1}{5}}$ .

${({(27 (x - 2))}^{\frac{1}{5}})}^{5} = 3^{5}$

Simplify the left side.

Simplify ${({(27 (x - 2))}^{\frac{1}{5}})}^{5}$ .

Multiply the exponents in ${({(27 (x - 2))}^{\frac{1}{5}})}^{5}$ .

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

${(27 (x - 2))}^{\frac{1}{5} \cdot 5} = 3^{5}$

Cancel the common factor of $5$ .

Cancel the common factor.

${(27 (x - 2))}^{\frac{1}{5} \cdot 5} = 3^{5}$

Rewrite the expression.

${(27 (x - 2))}^{1} = 3^{5}$

Apply the distributive property.

${(27 x + 27 \cdot - 2)}^{1} = 3^{5}$

Multiply.

Multiply $27$ by $- 2$ .

${(27 x - 54)}^{1} = 3^{5}$

Simplify.

$27 x - 54 = 3^{5}$

Simplify the right side.

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

$27 x - 54 = 243$

Step 3

Solve for $x$ .

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

Add $54$ to both sides of the equation.

$27 x = 243 + 54$

Add $243$ and $54$ .

$27 x = 297$

Divide each term in $27 x = 297$ by $27$ and simplify.

Divide each term in $27 x = 297$ by $27$ .

$\frac{27 x}{27} = \frac{297}{27}$

Simplify the left side.

Cancel the common factor of $27$ .

Cancel the common factor.

$\frac{27 x}{27} = \frac{297}{27}$

Divide $x$ by $1$ .

$x = \frac{297}{27}$

Simplify the right side.

Divide $297$ by $27$ .

$x = 11$

Solve for x fifth root of 27(x-2)=3

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