Question 472912
(24xy)<sup>(-5/6)</sup> would be equal to 1 / (24xy)<sup>(5/6)</sup>
this is because {{{x^(-a)}}} is equal to {{{1/x^a}}}
it's one of the laws of exponents.
if the term with the negative exponent is in the numerator, then place it in the denominator.
if the term with the negative exponent is in the denominator, then place it in the numerator.
since (24xy) is in parentheses, then it is the term that is being raised to the negative exponent.
if 24xy was not enclosed in parentheses, then only the immediate term to the left of the exponent would be moved.
example:
24xy<sup>(-5/6)</sup> would be equal to 24x / y<sup>(5/6)</sup>
to confirm that the transformation is correct, simply provide a value for x and y and solve both the initial configuration and the final configuration.
example:
x = 5
y = 8
(24xy)^(-5/6) = 24*5*8)^(-5/6) = 960^(-5/6) = .003271704
1/(24xy)^(5/6) = 1/(24*5*8)^(5/6) = 1/960^(5/6) = 1/305.6511453 = .003271704