Respuesta :
Option A
[tex]\left(y^{\frac{4}{3}} \cdot y^{\frac{2}{3}}\right)^{\frac{-1}{2}} = \left(y^{2}\right)^{\frac{-1}{2}}[/tex]
Solution:
Given expression is:
[tex]\left(y^{\frac{4}{3}} \cdot y^{\frac{2}{3}}\right)^{\frac{-1}{2}}[/tex]
Product of powers property:
The product of powers property tells us that when you multiply powers with the same base you just have to add the exponents
Which is represented as,
[tex]a^m.a^n = a^{m+n}[/tex]
Therefore, the given expression becomes,
[tex]\left(y^{\frac{4}{3}+\frac{2}{3}}\right)^{\frac{-1}{2}}[/tex]
Now add the exponents, we get
[tex]\left(y^{\frac{4+2}{3}}\right)^{\frac{-1}{2}}[/tex]
Simplify the above expression
[tex]\left(y^{\frac{6}{3}}\right)^{\frac{-1}{2}}[/tex]
Simplify the exponent of y, we get
[tex]\left(y^{2}\right)^{\frac{-1}{2}}[/tex]
Thus Option A is correct
