Question

What is 20x^6 divided by 14x^2

Answer 1

`(10)/(7)x^4`

Explanation:

Exponent Rules:

There is an exponent rule which essentially states:
`(x^a)/(x^b)=x^(a-b)`

All this is doing is essentially cancelling out the terms, since you can think of it as:
`(x^a)/(x^b)\implies \frac{x*x*x...\text{`, and if you recall, multiplication and division cancel. So we cancel out "b" amount of x's, leaving us with "a - b" amount of x's. Which can also be expressed as:
`x^(a-b)`

We can use this logic to solve our problem:
`(20x^6)/(14x^2)`, here we can separate this into two different fractions:
`(20)/(14)*(x^6)/(x^2)` and we can use basic division on the left side and our exponent rule on the right side. This gives us the following:
`(10)/(7)x^(6-2)\implies (10)/(7)x^4` which is our solution!