Question

How do you divide `20m ^ { 5} n ^ { 8} 0^ { 4} \div 2m ^ { 2} n ^ { 6} o^ { 3}`?

Answer 1

See a solution process below:

(Assuming `o^4` and `o^3` are the letter `o` and not the number `0`)

Explanation:

First, rewrite the expression as:

`(20m^5n^8o^4)/(2m^2n^6o^3) => 20/2(m^5/m^2)(n^8/n^6)(o^4/o^3) =>`

`10(m^5/m^2)(n^8/n^6)(o^4/o^3)`

Next, use this rule of exponents to divide the `m`, `n` and `o` terms:

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

`10(m^color(red)(5)/m^color(blue)(2))(n^color(red)(8)/n^color(blue)(6))(o^color(red)(4)/o^color(blue)(3)) => 10m^(color(red)(5)-color(blue)(2))n^(color(red)(8)-color(blue)(6))o^(color(red)(4)-color(blue)(3)) =>`

`10m^3n^2o^1`

Now, use this rule of exponents to simplify the `o` term:

`a^color(red)(1) = a`

`10m^3n^2o^color(red)(1) =>`

`10m^3n^2o`