To find the missing value in the equation [tex]\( x^{\frac{1}{5}} = 6 \)[/tex], we need to isolate [tex]\( x \)[/tex].
Here is the step-by-step process:
1. The given equation is [tex]\( x^{\frac{1}{5}} = 6 \)[/tex].
2. To solve for [tex]\( x \)[/tex], raise both sides of the equation to the power of 5. This will help us eliminate the fractional exponent on [tex]\( x \)[/tex]. Mathematically, this step looks like:
[tex]\[
\left(x^{\frac{1}{5}}\right)^5 = 6^5
\][/tex]
3. On the left side of the equation, raising [tex]\( x^{\frac{1}{5}} \)[/tex] to the power of 5 results in [tex]\( x \)[/tex]:
[tex]\[
x = 6^5
\][/tex]
4. Now we need to calculate [tex]\( 6^5 \)[/tex].
5. The value of [tex]\( 6^5 \)[/tex] is [tex]\( 7776 \)[/tex].
So, the missing value in [tex]\( x^{\frac{1}{5}} = 6 \)[/tex] is [tex]\( x = 7776 \)[/tex].
