Solve for x 2 fifth root of 5x+2-1=3

$2 \sqrt[5]{5 x + 2} - 1 = 3$

Step 1

Move all terms not containing $2 \sqrt[5]{5 x + 2}$ to the right side of the equation.

Add $1$ to both sides of the equation.

$2 \sqrt[5]{5 x + 2} = 3 + 1$

Add $3$ and $1$ .

$2 \sqrt[5]{5 x + 2} = 4$

Step 2

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

${(2 \sqrt[5]{5 x + 2})}^{5} = 4^{5}$

Step 3

Simplify each side of the equation.

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

${(2 {(5 x + 2)}^{\frac{1}{5}})}^{5} = 4^{5}$

Simplify the left side.

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

Apply the product rule to $2 {(5 x + 2)}^{\frac{1}{5}}$ .

$2^{5} {({(5 x + 2)}^{\frac{1}{5}})}^{5} = 4^{5}$

Raise $2$ to the power of $5$ .

$32 {({(5 x + 2)}^{\frac{1}{5}})}^{5} = 4^{5}$

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

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

$32 {(5 x + 2)}^{\frac{1}{5} \cdot 5} = 4^{5}$

Cancel the common factor of $5$ .

Cancel the common factor.

$32 {(5 x + 2)}^{\frac{1}{5} \cdot 5} = 4^{5}$

Rewrite the expression.

$32 {(5 x + 2)}^{1} = 4^{5}$

Simplify.

$32 (5 x + 2) = 4^{5}$

Apply the distributive property.

$32 (5 x) + 32 \cdot 2 = 4^{5}$

Multiply.

Multiply $5$ by $32$ .

$160 x + 32 \cdot 2 = 4^{5}$

Multiply $32$ by $2$ .

$160 x + 64 = 4^{5}$

Simplify the right side.

Raise $4$ to the power of $5$ .

$160 x + 64 = 1024$

Step 4

Solve for $x$ .

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

Subtract $64$ from both sides of the equation.

$160 x = 1024 - 64$

Subtract $64$ from $1024$ .

$160 x = 960$

Divide each term in $160 x = 960$ by $160$ and simplify.

Divide each term in $160 x = 960$ by $160$ .

$\frac{160 x}{160} = \frac{960}{160}$

Simplify the left side.

Cancel the common factor of $160$ .

Cancel the common factor.

$\frac{160 x}{160} = \frac{960}{160}$

Divide $x$ by $1$ .

$x = \frac{960}{160}$

Simplify the right side.

Divide $960$ by $160$ .

$x = 6$

Solve for x 2 fifth root of 5x+2-1=3

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