How do you simplify #((-7^2 r^5 s^-3)/( 3^-1 r^-4 s^4))^4#?

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Answer 1 · 2015-07-11T23:04:44

#A=((147^4)*r^36)/(s^28)#

Let's go to simplify : #A=((-7^2r^5s^(-3))/(3^(-1)r^(-4)s^4))^4#

First, use this properties :
#->##color(red)(a^(-n) = 1/a^n)#
#->##color(red)(1/a^(-n) = a^n)#

#A=((-7^2*color(red)(3^1)r^5color(red)(r^4))/(s^4color(red)(s^3)))^4#

Second, simplify #A# with that :

#color(blue)(a^n*a^m=a^(n+m))#

#A=((-49*3*color(blue)(r^9))/(color(blue)(s^7)))^4#

Finally, apply the power #4# to the fraction inside the parenthesis, with :

#color(green)((kxxa^x)^y=k^yxxa^(x*y))#

#A=((-147)^4*color(green)(r^36))/(color(green)(s^28))#
# #
# #
Therefore :

#A=(466948881*r^36)/(s^28)#