Question

Divide 12x 4 y 4 by 3x 2 y. A. 4x 6y 5 B. 4x 2y 3 C. 9x 6 D. 9x 2y 3

Answer 1

`(12x^4y^4)/(3x^2y)=4x^2y^3`

Explanation:

Consider an element
`a\\eq 0`

We know that
`(a^m)/(a^n)=a^(m-n)`

Here, m and n are exponents and a is a base. Exponent refers to the no. of times a term is multiplied by itself. Another word for exponents is powers.

Other Properties of exponents:

`a^m* a^n=a^(m+n)\\a^0=1\\\left ( a^m \right )^n=a^(mn)`

Here, we are required to divide
`12x^4y^4` by
`3x^2y`.

Consider
`(12x^4y^4)/(3x^2y)`

We will solve
`(12)/(3)\,,\,(x^4)/(x^2)\,,\,(y^4)/(y)` separately.

Here,

`(12)/(3)=4\\(x^4)/(x^2)=x^(4-2)=x^2\\(y^4)/(y)=y^3`

So,
`(12x^4y^4)/(3x^2y)=4x^2y^3`