To solve for [tex]\( x \)[/tex] in the equation [tex]\( x^{\frac{1}{3}} = 16 \)[/tex], follow these steps:
1. Understand the Equation: The given equation is [tex]\( x^{\frac{1}{3}} = 16 \)[/tex]. This means that the cube root of [tex]\( x \)[/tex] is equal to 16.
2. Isolate [tex]\( x \)[/tex]: To isolate [tex]\( x \)[/tex], we need to remove the cube root. We can do this by raising both sides of the equation to the power of 3. This operation will cancel out the cube root on the left-hand side.
[tex]\[
(x^{\frac{1}{3}})^3 = 16^3
\][/tex]
3. Simplify the Equation: Simplifying the left-hand side, we get:
[tex]\[
x = 16^3
\][/tex]
4. Calculate [tex]\( 16^3 \)[/tex]: Now, we need to compute [tex]\( 16^3 \)[/tex].
[tex]\[
16^3 = 16 \times 16 \times 16
\][/tex]
Break it down step by step:
[tex]\[
16 \times 16 = 256
\][/tex]
Then:
[tex]\[
256 \times 16 = 4096
\][/tex]
So, [tex]\( 16^3 = 4096 \)[/tex].
Therefore, the solution is:
[tex]\[
x = 4096
\][/tex]
So, the value of [tex]\( x \)[/tex] is [tex]\( \boxed{4096} \)[/tex].
