What is 4s over 3t to the negative 2nd power times 2s over 6t to the 2nd power? The format is a bit weird .

Question

#((4s)/(3t))^(-2) xx ((2s)/(6t))^2#

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Answer 1 · 2018-04-18T22:35:08

#1/16#

#((4s)/(3t))^(-2)*((2s)/(6t))^2#

First when given a negative exponent, I reciprocate the expression and make the exponent positive, so:

#((3t)/(4s))^(2)*((2s)/(6t))^2#

#(3t)^2/(4s)^2*(2s)^2/(6t)^2#

#((3t)(3t))/((4s)(4s))*((2s)(2s))/((6t)(6t))#

#(9t^2)/(16s^2)*(4s^2)/(36t^2)#

Cross simplify:

#(cancel(9t^2))/(cancel(16s^2)4)*(cancel(4s^2))/(cancel(36t^2)4)=#

#1/16#