How do you simplify #(\frac { 3s ^ { - 2} t ^ { 7} } { 6s ^ { 3} t ^ { - 5} } ) ^ { - 4}#?

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Answer 1 · 2016-10-31T20:04:39

#(16s^20)/(t^48)#

Refer below for the laws of indices which are used in this answer:

Before we start simplifying inside the bracket, lets do something with the index of #-4#

#((3s^-2t^7)/(6s^3t^-5))^color(red)(-4) = ((6s^3t^-5)/(3s^-2t^7))^color(red)(4)#

Now look inside the bracket:

#((6s^3t^-5)/(3s^-2t^7))^color(red)(4) = ((2s^3xxs^2)/(t^7xxt^5))^color(red)(4)#

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

=#(2^4s^20)/(t^48)#

=#(16s^20)/(t^48)#

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Recall the laws of indices:

#(x^m)^n = x^(mxxn)#

#x^-m = 1/x^m and 1/x^-n = x^n#

#(a/b)^-1 = b/a" "larr# invert the entire fraction in a bracket
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