Question

i dont mean to throw 2 problems at yall but i do not get this whatsoever. can someone help and give a simple step by step?

Answer 1

To answer the first expression we first need to remeber the following rule

$(ab)^n=a^nb^n$

Then

$\begin{gathered} (2x^{\frac{3}{5}})^2=2^2(x^{\frac{3}{5}})^2 \\ =4(x^{\frac{3}{5}})^2 \end{gathered}$

now, we need to remember the rule:

$(a^n)^m=a^{nm}$

hence,

$\begin{gathered} (2x^{\frac{3}{5}})^2=4(x^{\frac{3}{5}})^2 \\ =4x^{\frac{3}{5}\cdot2} \\ =4x^{\frac{6}{5}} \end{gathered}$

To do the second one we apply the same rules:

$\begin{gathered} (x^{\frac{1}{4}}\cdot y^{\frac{1}{3}})^3=(x^{\frac{1}{4}})^3(y^{\frac{1}{3}})^3 \\ =x^{\frac{1}{4}\cdot3}y^{\frac{1}{3}\cdot3} \\ =x^{\frac{3}{4}}y^{\frac{3}{3}} \\ =x^{\frac{3}{4}}y^1 \\ =x^{\frac{3}{4}}y \end{gathered}$