Questions: Solve. x^(1 / 4) = 4 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution(s) is/are (Type an integer or a simplified fraction. Use a comma to separate answers.) B. There is no solution.

Solve. x^(1 / 4) = 4 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution(s) is/are (Type an integer or a simplified fraction. Use a comma to separate answers.) B. There is no solution.
Transcript text: Solve. \[ x^{1 / 4}=4 \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution(s) is/are $\square$ (Type an integer or a simplified fraction. Use a comma to separate answers.) B. There is no solution.
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Solution

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Solution Steps

To solve the equation \( x^{1/4} = 4 \), we need to isolate \( x \). This can be done by raising both sides of the equation to the power of 4, which will eliminate the fractional exponent on the left side. This will give us the value of \( x \).

Step 1: Understand the Given Equation

The given equation is \( x^{1/4} = 4 \). This means that the fourth root of \( x \) is equal to 4.

Step 2: Eliminate the Fractional Exponent

To solve for \( x \), we need to eliminate the fractional exponent by raising both sides of the equation to the power of 4. This gives us: \[ (x^{1/4})^4 = 4^4 \]

Step 3: Simplify the Equation

Simplifying the left side, we have: \[ x = 4^4 \]

Step 4: Calculate the Value of \( x \)

Calculate \( 4^4 \): \[ 4^4 = 256 \]

Final Answer

\(\boxed{256}\)

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