To simplify and use positive
power:{[125x^(1/2)y^(-1/3)]^(-2/3) }
{x^(1/3)*y^(-2/3)}
Solution:
First
bracket:
{125x^(1/2) y^(-1/3)
}^(-2/3)
= 125^(-2/3) *x^(1/2*(-2/3))
*y((-1/3*(-2/3).
= (5^3)^(-2/3) * x^(-1/3)*y(2/9), as
a^m)^n = a^(mn)
=5^(-2) * x^ (-1/3) *
y^(2/9).............(1)
2nd bracket :
x^(1/3)*y^(-2/3)..........(2)
So the given expression =
{5^(-2) *x^(-1/3)*y^(2/9)}*{x^(1/3)*y^(-2/3)}
We can
rearrange x's together and y 's together as multiplication is commutative and the
expression is
5^(-2)* (x^(-1/3)*x^(1/3))
(y^2/3)*y^(-2/3))
= (1/5^2). x ^(1/3 - 1/3)*
y^(2/9-6/9)
= 1/25
x^0*y^(-4/9) .
=1/(5^2* y^(4/9), as a^-m =
1/a^m.
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