Find All Complex Solutions 5x^(1/4)=30

$5 x^{\frac{1}{4}} = 30$

Step 1

Subtract $30$ from both sides of the equation.

$5 x^{\frac{1}{4}} - 30 = 0$

Step 2

Factor $5$ out of $5 x^{\frac{1}{4}} - 30$ .

Factor $5$ out of $5 x^{\frac{1}{4}}$ .

$5 (x^{\frac{1}{4}}) - 30 = 0$

Factor $5$ out of $- 30$ .

$5 x^{\frac{1}{4}} + 5 \cdot - 6 = 0$

Factor $5$ out of $5 x^{\frac{1}{4}} + 5 \cdot - 6$ .

$5 (x^{\frac{1}{4}} - 6) = 0$

Step 3

Divide each term in $5 (x^{\frac{1}{4}} - 6) = 0$ by $5$ and simplify.

Divide each term in $5 (x^{\frac{1}{4}} - 6) = 0$ by $5$ .

$\frac{5 (x^{\frac{1}{4}} - 6)}{5} = \frac{0}{5}$

Simplify the left side.

Cancel the common factor.

$\frac{5 (x^{\frac{1}{4}} - 6)}{5} = \frac{0}{5}$

Divide $x^{\frac{1}{4}} - 6$ by $1$ .

$x^{\frac{1}{4}} - 6 = \frac{0}{5}$

Simplify the right side.

Divide $0$ by $5$ .

$x^{\frac{1}{4}} - 6 = 0$

Step 4

Add $6$ to both sides of the equation.

$x^{\frac{1}{4}} = 6$

Step 5

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

${(x^{\frac{1}{4}})}^{4} = 6^{4}$

Step 6

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, ${(a^{m})}^{n} = a^{m n}$ .

$x^{\frac{1}{4} \cdot 4} = 6^{4}$

Cancel the common factor of $4$ .

Cancel the common factor.

$x^{\frac{1}{4} \cdot 4} = 6^{4}$

Rewrite the expression.

$x^{1} = 6^{4}$

Simplify.

$x = 6^{4}$

Simplify the right side.

Raise $6$ to the power of $4$ .

$x = 1296$

Find All Complex Solutions 5x^(1/4)=30

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