How do you simplify #(4/7m)^2(49m)(17p)(1/34p^5)#?

1 Answer
Feb 27, 2017

Answer:

See the entire solution process below:

Explanation:

First, we will use these rules for exponents to simplify the term on the left: #color(red)((4/7m)^2)#: #a = a^color(red)(1)# and #(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))#

#color(red)((4/7m)^2)(49m)(17p)(1/34p^5) =#

#color(red)((4^1/7^1m^1)^color(blue)(2))(49m)(17p)(1/34p^5) =#

#color(red)((4^(1xxcolor(blue)(2))/7^(1xxcolor(blue)(2))m^(1xxcolor(blue)(2)))(49m)(17p)(1/34p^5) = #

#(4^2/7^2m^2)(49m)(17p)(1/34p^5) = #

#(16/49m^2)(49m)(17p)(1/34p^5)#

Next, we can rewrite this expression as:

#(16/49m^2 xx 49m)(17p xx 1/34p^5)#

Then, factor and cancel the coefficients:

#(16/color(red)(cancel(color(black)(49)))m^2 xx color(red)(cancel(color(black)(49)))m)(color(blue)(cancel(color(black)(17)))p xx 1/(color(blue)(cancel(color(black)(17)))2)p^5) =#

#(16m^2 xx m)(p xx 1/2p^5)#

We can then use this rule of exponents to simplify the variables:

#x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))#

#(16m^color(red)(2) xx m^color(blue)(1))(p^color(red)(1) xx 1/2p^color(blue)(5)) =#

#(16m^(color(red)(2)+color(blue)(1)))(1/2p^(color(red)(1)+color(blue)(5))) =#

#(16m^3)(1/2p^6)#=#

#(16m^3p^6)/2 =#

#8m^3p^6#