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

2 Answers

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

Explanation:

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

Jun 19, 2017

#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)#