Answer: See the below steps for simplifying to [tex]2^{\frac{2}{3}-\frac{x}{3} }[/tex].
Step-by-step explanation:
We will simplify the given expression to reach the requested result. For this we will use the exponent rules, which I have outlined below.
[tex]\text{Exponent Rules: } \boxed{(x^m)^n=x^{m*n}}\;\;\boxed{x^mx^n=x^{m+n}}\;\;\boxed{\frac{x^m}{x^n}=x^{m-n} }\;\; \boxed{x^{-m}=\frac{1}{x^m} }[/tex]
Given:
[tex]\displaystyle (2^{\frac{1}{3} })^{2-x}[/tex]
Apply the power to a power rule:
[tex]\boxed{(x^m)^n=x^{m*n}}[/tex]
[tex]\displaystyle 2^{(\frac{1}{3}*(2-x) )}[/tex]
Distribute the one-third:
[tex]\displaystyle 2^{\dfrac{2}{3}-\dfrac{x}{3} }[/tex]