which expression is equivalent to

Question

(8w⁷x^-5y³z^-9)^-2/3

Answer 1

Multiplies the exponents:

8^(-2/3) = 1 over 8^(2/3) = 1 over [cube root(8)]^2 = 1 / 2^2 = 1/4

w^ (-14/3) , so w^(14/3) goes to the denominator

x^(10/3) stays in the numerator

y^-2, so y^2 goes to the denominator

z^6 stays in the numerator

the fraction is

x^(10/3) z^6
-------------------
4 w^ 14/3 y^2

The only question that remains is to possibly rationalize the denominator since w^14/3
may be irrational

Answer 2

8^2/3 = 4

 

(w⁷)^-2/3 = w^-14/3 = 1/w^14/3

 

(x^-5)^-2/3 = x^10/3

 

(y³)^-2/3 = y^-2 = 1/y²

 

(z^-9)^-2/3 = z⁶

 

4x^10/3z⁶/w^14/3y²