Let's work through the problem step-by-step and simplify the expression to find the value of \( x \).
1. Innermost group, apply the product of powers:
[tex]\[
\left[3^{-1}\right]^3
\][/tex]
When you raise a power to a power, you multiply the exponents:
[tex]\[
(3^{-1})^3 = 3^{-1 \cdot 3} = 3^{-3}
\][/tex]
2. Apply the power of a power:
[tex]\[
3^{-3}
\][/tex]
We have already simplified to \( 3^{-3} \) in the previous step.
3. Apply the negative exponent:
[tex]\[
\frac{1}{3^3}
\][/tex]
A negative exponent means that we take the reciprocal of the base with a positive exponent.
4. Simplify:
[tex]\[
\frac{1}{3^3} = \frac{1}{27}
\][/tex]
Here, \( 3^3 \) equals 27.
So, the value of \( x \) in the simplified expression is:
[tex]\[
x = 27
\][/tex]
Thus, [tex]\( x = 27 \)[/tex].
