Question

Laws of exponent - divisionsimplify27x³y⁵_____18x⁴y²

Answer 1

`(3)/(2)x^(-1)y^(-1)\text{ or }(3)/(2xy)`

1) Let's write that expression, and before dealing with the exponents we can simplify 27, and 18 since both are divisible by 9

`(27x^3y)/(18x^4y^2)=(3x^3y)/(2x^4y^2)`

2) Now we can subtract those exponents since it is a division:

`(3x^3y)/(2x^4y^2)=(3)/(2)x^(3-4)y^(1-2)=(3)/(2)x^(-1)y^(-1)`

We can write like this

`\begin{gathered} (3)/(2)x^(-1)y^(-1)=(3)/(2)\cdot(1)/(x)\cdot(1)/(y)=\text{ }(3)/(2xy) \\ (3)/(2)x^(-1)y^(-1)\text{ or }(3)/(2xy) \end{gathered}`

Both forms are equally correct.