Question

How do you simplify `(\frac { 3x ^ { 4} y ^ { - 8} } { 6^ { - 1} x ^ { - 2} y } ) ^ { - 2}`?

Answer 1

`1/2 * x^(-12) * y^(18)`

Explanation:

`3/6 * x^(4(-2) - (-2)(-2)) * y^((-8)(-2) + 2)`

Answer 2

`y^18/(324x^12)`

Explanation:

There are quite a number of laws of indices being applied here.

• `(a/b)^-m = (b/a)^(+m)" "larr` invert the fraction, positive index

`((3x^4y^-8)/(6^-1x^-2y))^-2 = ((6^-1x^-2y)/(3x^4y^-8))^2`

• `x^-m = 1/x^m and 1/y^-n = y^n`

Make all the negative indices positive

`((6^-1x^-2y)/(3x^4y^-8))^2 = ((yxxy^8)/(3xx6x^4x^2))^2 = (y^9)/(18x^6)`

• `(x^m)^n = x^(mxxn)" "larr` multiply the indices

`((y^9)/(18x^6))^2 = (y^18)/(18^2 x^12`

`y^18/(324x^12)`