Solve for x fourth root of 5x-4=1

$\sqrt[4]{5 x} - 4 = 1$

Move all terms not containing $\sqrt[4]{5 x}$ to the right side of the equation.

Add $4$ to both sides of the equation.

$\sqrt[4]{5 x} = 1 + 4$

Add $1$ and $4$ .

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

To remove the radical on the left side of the equation, raise both sides of the equation to the power of $4$ .

${\sqrt[4]{5 x}}^{4} = 5^{4}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{5 x}$ as ${(5 x)}^{\frac{1}{4}}$ .

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

Simplify the left side.

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

Multiply the exponents in ${({(5 x)}^{\frac{1}{4}})}^{4}$ .

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

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

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

${(5 x)}^{1} = 5^{4}$

Simplify.

$5 x = 5^{4}$

Simplify the right side.

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

$5 x = 625$

Divide each term in $5 x = 625$ by $5$ and simplify.

Divide each term in $5 x = 625$ by $5$ .

$\frac{5 x}{5} = \frac{625}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{625}{5}$

Divide $x$ by $1$ .

$x = \frac{625}{5}$

Simplify the right side.

Divide $625$ by $5$ .

$x = 125$