Solve for x x^(1/4)+3=0

$x^{\frac{1}{4}} + 3 = 0$

Subtract $3$ from both sides of the equation.

$x^{\frac{1}{4}} = - 3$

Raise each side of the equation to the power of $4$ to eliminate the fractional exponent on the left side.

${(x^{\frac{1}{4}})}^{4} = {(- 3)}^{4}$

Simplify the exponent.

Simplify the left side.

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

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

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

$x^{\frac{1}{4} \cdot 4} = {(- 3)}^{4}$

Cancel the common factor of $4$ .

Cancel the common factor.

$x^{\frac{1}{4} \cdot 4} = {(- 3)}^{4}$

Rewrite the expression.

$x^{1} = {(- 3)}^{4}$

Simplify.

$x = {(- 3)}^{4}$

Simplify the right side.

Raise $- 3$ to the power of $4$ .

$x = 81$

Exclude the solutions that do not make $x^{\frac{1}{4}} + 3 = 0$ true.

$No solution$