[tex](x^{\frac{4}{3}}x^{\frac{2}{3}})^{\frac{1}{3}} = x^{\frac{2}{3}[/tex]
Solution:
Given expression is:
[tex]\displaystyle (x^{\frac{4}{3}}x^{\frac{2}{3}})^{\frac{1}{3}}[/tex]
We have to find the equivalent expression
We can simplify the above expression using law of exponents
Use the following law of exponents:
[tex]a^m \times a^n = a^{m+n}[/tex]
Therefore,
[tex]\displaystyle (x^{\frac{4}{3}}x^{\frac{2}{3}})^{\frac{1}{3}} = (x^{\frac{4}{3}+\frac{2}{3}})^{\frac{1}{3}}\\\\Simplify\\\\\displaystyle (x^{\frac{4}{3}}x^{\frac{2}{3}})^{\frac{1}{3}} = (x^2)^\frac{1}{3}[/tex]
Use another law of exponent
[tex](a^m)^n = a^{mn}[/tex]
Therefore,
[tex](x^{\frac{4}{3}}x^{\frac{2}{3}})^{\frac{1}{3}} = x^{\frac{2}{3}[/tex]
Thus the equivalent expression is found
