Respuesta :

Answer:

C

Step-by-step explanation:

Using exponential properties, we multiply 1/5 by the exponents 8 and 8 to get (x^(8/5))*(y^(8/5)). Note that when you square root x, it is the same as x to the power of 1/2. Same for cubing, etc. So, x^(8/5)=x^(8*(1/5))= fifth root of x^8. The same would happen to y^(8/5), which is the fifth root of (y^8). So, the expression ends up as the fifth root of x^8 times the fifth root of y^8. Simplifying it, they can both go under one of the fifth roots instead of two, since they have the same exponents and fifth root. So, we get to answer choice C. (Sorry, I don't really know how to say the square root but with a 5. Not sure if there is a more mathematical way of saying it.) Hope this helps!

semsee45

Answer:

C

Step-by-step explanation:

[tex](x^8y^8)^{\frac15}[/tex]

Apply exponent rule  [tex]a^nb^n=(a \cdot b)^n[/tex] :

[tex]\implies((xy)^8)^\frac15[/tex]

Apply exponent rule [tex](a^b)^c=a^{bc}[/tex] :

[tex]\implies(xy)^\frac85[/tex]

Apply rule  [tex]a^\frac1n=\sqrt[n]{a}[/tex] :

[tex]\implies(\sqrt[5]{xy})^8[/tex]