Answer:
Thus, [tex](x^{\frac{4}{3}}x^{\frac{2}{3}})^{\frac{1}{3}}[/tex] is equivalent to [tex]x^{\frac{2}{3}}[/tex]
Step-by-step explanation:
Consider the given expression
[tex](x^{\frac{4}{3}}x^{\frac{2}{3}})^{\frac{1}{3}}[/tex]
Using property of exponents [tex]a^ma^n=a^{m+n}[/tex]
Here, a = x , [tex]m=\frac{4}{3} , n=\frac{2}{3}[/tex]
[tex](x^{\frac{4}{3}}x^{\frac{2}{3}})^{\frac{1}{3}}=(x^{\frac{4}{3}+\frac{2}{3}})^\frac{1}{3}[/tex]
Solving further,
[tex]\Rightarrow (x^{\frac{4+2}{3}})^\frac{1}{3}[/tex]
[tex]\Rightarrow (x^{\frac{6}{3}})^\frac{1}{3}[/tex]
[tex]\Rightarrow (x^2)^\frac{1}{3}[/tex]
Again using property of exponents [tex](a^m)^n=a^{mn}[/tex]
We get , [tex](x^2)^\frac{1}{3}=x^{\frac{2}{3}}[/tex]
Thus, [tex](x^{\frac{4}{3}}x^{\frac{2}{3}})^{\frac{1}{3}}[/tex] is equivalent to [tex]x^{\frac{2}{3}}[/tex]
