Question

(x^-2 y^3 / x^2 y)^-1/2 (x^3 y / y^1/2)?

Answer 1

\[(((x^{-2} y^3) / ((x^2 y))^{-1/2})) \times ((x^3 y) / (y^{1/2}))? \]
\[\Huge \frac {1}{\sqrt \frac {x^{-2} y^3} {x^2 y}} \times \frac{x^3 y} { y^{1/2}} \]

Answer 2

why is the first one in square root?

Answer 3

k this is a crazy long equation, so im gonna break it down piece at a time then build it back together so u can see where all the bitz go...
\[ \large (x^-2 y^3 / x^2 y)^{-1/2} (x^3 y / y^1/2)? \] so x^-2 y^3
\[\large = \frac {y^3}{x^2} \]
and x^2 y
\[\large = x^2 \times y \]
now to the power of half = square root
ie \[\large 4^{1/2} = \sqrt 4 = 2\]
and anything to a negative power = 1/ that thing to the positive power
ie \[\large 4^{-1/2} = \frac {1} {\sqrt 4} = \frac 12\]
following so far?

Answer 4

so the 2y^2 is = 1/2 ?

Answer 5

\[ \large (x^{-2} y^3 / x^2 y)^{-1/2} (x^3 y / y^1/2)? \]
so x^-2 y^3
\[\large = \frac {y^3}{x^2} \]
and x^2 y
\[\large = x^2 \times y \]
so first section of equation = (x^{-2} y^3 / x^2 y)^{-1/2}
\[\Huge =(\frac {\frac {y^3}{x^2}} {x^2 \times y})^{-1/2}\]
\[\Huge = \frac {1}{\sqrt {(\frac {\frac {y^3}{x^2}} {x^2 \times y})}}\]
with me so far?

Answer 6

sorry my laptop froze

Answer 7

so since its -1/2 they are all moved to the bottom?

Answer 8

sorry, it was getting exhausting typing in latex, gonna basic it down just to powers in plain form:
first part :-

x^-2 y^3 / x^2 y
=x^-2 * y^3 * x^-2 * y^-1
=x^-4 * y^2
= y^2 / x^4

so
(x^-2 y^3 / x^2 y)^-1/2
= ( x^-4 * y^2 )^-1/2
= ( x^2 * y^-1)
= ( x^2 / y )

2nd part:
(x^3 y / y^1/2)
=( x^3 * y * y^(-1/2) )
= x^3 * y^(1/2)

so together
1st part times 2nd part:
(x^-2 y^3 / x^2 y)^-1/2 * (x^3 y / y^1/2)
= ( x^2 / y ) * x^3 * y^(1/2)
= x^2 * y^-1 * x^3 * y^(1/2)
= x^5 * y^-(1/2)
= x^5 / y^1/2
\[ \huge \frac {x^5}{ \sqrt y } \]

Answer 9

so that should be the final answer, and everything above was just a manipulation of powers rules

Answer 10

@Ssusu

Answer 11

I will look over it and make sure I got it thank you and I know this equation was long and annoying lol

Answer 12

sáll good ;) np