Question

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

Answer 1

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`