Solve for x 4(x+2)^(1/5)-1=7

$4 {(x + 2)}^{\frac{1}{5}} - 1 = 7$

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

Add $1$ to both sides of the equation.

$4 {(x + 2)}^{\frac{1}{5}} = 7 + 1$

Add $7$ and $1$ .

$4 {(x + 2)}^{\frac{1}{5}} = 8$

Raise each side of the equation to the power of $5$ to eliminate the fractional exponent on the left side.

${(4 {(x + 2)}^{\frac{1}{5}})}^{5} = 8^{5}$

Simplify the exponent.

Simplify the left side.

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

Apply the product rule to $4 {(x + 2)}^{\frac{1}{5}}$ .

$4^{5} {({(x + 2)}^{\frac{1}{5}})}^{5} = 8^{5}$

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

$1024 {({(x + 2)}^{\frac{1}{5}})}^{5} = 8^{5}$

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

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

$1024 {(x + 2)}^{\frac{1}{5} \cdot 5} = 8^{5}$

Cancel the common factor of $5$ .

Cancel the common factor.

$1024 {(x + 2)}^{\frac{1}{5} \cdot 5} = 8^{5}$

Rewrite the expression.

$1024 {(x + 2)}^{1} = 8^{5}$

Simplify.

$1024 (x + 2) = 8^{5}$

Apply the distributive property.

$1024 x + 1024 \cdot 2 = 8^{5}$

Multiply $1024$ by $2$ .

$1024 x + 2048 = 8^{5}$

Simplify the right side.

Raise $8$ to the power of $5$ .

$1024 x + 2048 = 32768$

Solve for $x$ .

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

Subtract $2048$ from both sides of the equation.

$1024 x = 32768 - 2048$

Subtract $2048$ from $32768$ .

$1024 x = 30720$

Divide each term in $1024 x = 30720$ by $1024$ and simplify.

Divide each term in $1024 x = 30720$ by $1024$ .

$\frac{1024 x}{1024} = \frac{30720}{1024}$

Simplify the left side.

Cancel the common factor of $1024$ .

Cancel the common factor.

$\frac{1024 x}{1024} = \frac{30720}{1024}$

Divide $x$ by $1$ .

$x = \frac{30720}{1024}$

Simplify the right side.

Divide $30720$ by $1024$ .

$x = 30$

Solve for x 4(x+2)^(1/5)-1=7

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