(5x/4y)^-3
To simplify the expression (5x/4y)^-3, we can use the rule that states: (a/b)^-n = (b/a)^n
Applying this rule:
(5x/4y)^-3 = (4y/5x)^3
Alternatively, we can also write (5x/4y)^-3 as the reciprocal of (5x/4y)^3:
(5x/4y)^-3 = 1 / (5x/4y)^3 = 1 / (125x^3 / 64y^3)
Now, to divide by a fraction, we multiply by the reciprocal of that fraction:
1 / (125x^3 / 64y^3) = 1 * (64y^3 / 125x^3)
Simplifying further:
64y^3 / 125x^3 = (2^6 * y^3) / (5^3 * x^3)
= (2^6 * y^3) / (125 * x^3)
= (64 * y^3) / (125 * x^3)
Therefore, (5x/4y)^-3 simplifies to (64y^3) / (125x^3).