Question

How do you simplify `(45mn^3) /( 20n^7)`?

Answer 1

You cancel terms that are common to the numerator and denominator.

Explanation:

Your initial expression looks like this

`(45mn^3)/(20n^7)`

You can simplify this expression by using the product of powers property of exponents

`color(blue)(x^(a + b) = x^a * x^b)`

to rewrite `n^7` as

`n^7 = n^3 * n^4`

Your expression now becomes

`(45mn^3)/(20n^7) = (45 * m * n^3)/(20 * n^3 * n^4) = (5 * 9 * m * n^3)/(5 * 4 * n^3 * n^4)`

Now all you have to do is cancel the terms that are common to the numerator and denominator to get

`(color(red)(cancel(color(black)(5))) * 9 * m * color(purple)(cancel(color(black)(n^3))))/(color(red)(cancel(color(black)(5))) * 4 * color(purple)(cancel(color(black)(n^3))) * n^4) = color(green)((9 * m)/(4 * n^4))`

Alternatively, you can write this as

`(9 * m)/(2n^2)^2`