How do you simplify #(10tu^-1v^-3w)/(t^-4u^-1v^-1w^0)#?

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Answer 1 · 2016-02-15T17:55:17

#=(10t^5w^(1))/v^2#

#(10tu^-1v^-3w)/(t^-4u^-1v^-1w^0#

#((10)xx(t^1u^-1v^-3w))/(t^-4u^-1v^-1w^0#

By property :
#color(blue)(a^m/a^n= a^(m-n)#

Applying the above to exponents of #t, u,v ,w#

#((10)xx(t^1u^-1v^-3w^1))/(t^-4u^-1v^-1w^0#

#=10xxt^(1 - (-4)) xx u^(-1-(-1)) xx v^(-3 -( -1)) xx w^((1-0)))#

#=10xxt^(1 +4) xx u^(-1 +1) xx v^(-3 +1) xx w^(1)#

#=10xxt^5 xx u^0 xx v^(-2) xx w^(1)#

As per property #color(blue)(a^0=1#

#=10xxt^5 xx color(blue)(1) xx v^(-2) xx w^(1)#

#=10t^5v^(-2) w^(1)#

#=(10t^5w^(1))/v^2#