How do you simplify #\frac { 12t ^ { 5} \times ( 6t ^ { 2} ) ^ { 2} } { 18t ^ { 2} }#?

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Answer 1 · 2017-06-04T00:53:50

#24t^7#

Expression#=(12t^5xx(6t^2)^2)/(18t^2)#

To simplify this expression we will use three of the laws of indices:

(i) #t^mxxt^n = t^(m+n)#
(ii) # (t^m)^n = t^(mxxn)#
(iii) #t^m/t^n = t^(m-n)#

Applying (ii)

Expression#= (12t^5xx6^2t^(2xx2))/(18t^2) =(12t^5xx36t^4)/(18t^2)#

#= (12t^5xx2t^4)/(t^2)#

Applying (i)

Expression#= (24t^(5+4))/(t^2) = (24t^9)/t^2#

Applying (iii)

Expression#= 24t^(9-2) = 24t^7#