Question

How do you simplify `\frac { 16p ^ { 2} r ^ { 3} } { 28p r ^ { 5} }`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`(16/28)(p^2/p)(r^3/r^5) =>`

`((4 xx 4)/(4 xx 7))(p^2/p)(r^3/r^5) =>`

`((color(red)(cancel(color(black)(4))) xx 4)/(color(red)(cancel(color(black)(4))) xx 7))(p^2/p)(r^3/r^5) =>`

`4/7(p^2/p)(r^3/r^5)`

Next, use these rules of exponents to simplify the `p` terms:

`a = a^color(blue)(1)` and `x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))` and `a^color(red)(1) = a`

`4/7(p^color(red)(2)/p^color(blue)(1))(r^3/r^5) => 4/7(p^(color(red)(2)-color(blue)(1)))(r^3/r^5) => 4/7(p^color(red)(1))(r^3/r^5) =>`

`4/7(p)(r^3/r^5) => (4p)/7(r^3/r^5)`

We can now use this rule of exponents to simplify the `r` terms:

`x^color(red)(a)/x^color(blue)(b) = 1/x^(color(blue)(b)-color(red)(a))`

`(4p)/7(r^color(red)(3)/r^color(blue)(5)) => (4p)/7(1/r^(color(blue)(5)-color(red)(3))) => (4p)/7(1/r^2) =>`

`(4p)/(7r^2)`