How do you multiply #t^ { - 1} u ^ { - 1} \cdot t u ^ { - 5} \cdot t ^ { - 4} u ^ { 0}#?

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Answer 1 · 2017-07-25T07:48:20

#=1/(t^4u^6)#

Recall two of the laws of indices.

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

#x^0 = 1" "(0^0# is undefined)

#color(red)(t^-1u^-1) xx tcolor(blue)(u^-5) xx color(green)(t^-4)color(magenta)(u^0)#

#= 1/(color(red)(tu)) xx t/color(blue)(u^5) xx 1/color(green)(t^4) xx color(magenta)(1)" "larr# all positive indices

#= 1/(canceltu) xx cancelt/u^5 xx 1/t^4#

#=1/(t^4u^6)#

Answer 2 · 2017-07-25T07:49:27

#t^(-1)u^(-1)*tu^(-5)*t^-4u^0=1/(t^4u^6#

#t^(-1)u^(-1)*tu^(-5)*t^-4u^0#

= #(t^(-1)*t^1*t^-4)*(u^(-1)*u^(-5)*u^0)#

= #t^(-1+1+(-4))*u^(-1+(-5)+0)#

= #t^(-4)*u^(-6)#

= #1/(t^4u^6#