Question

Fill in the blanks to create a true statement.
(125 x^3 y^-12)^-2/3=

Answer 1

Explanation:

Factorize 125 = 5 * 5 * 5 = 5³

`(125x^(3)*y^(-12))^{(-2)/(3)} = (5^(3)x^(3)*y^(-12))^{(-2)/(3)}\\\\ = 5^{(3*(-2)/(3))}* x^{[3*(-2)/(3)]}*y^{-12*(-2)/(3)}\\\\= 5^(-2) * x^(-2) * y^((-4*-2))\\\\=(1)/(5^(2)x^(2))*y^(8)\\\\=(y^(8))/(25x^(2))`

`(a*b)^(m) = a^(m)*b^(m)\\\\a^(-m)=(1)/(a^(m))`