Question

Multiply and simplify the following rational expression

2x^3y^6 . 15x2
5x^2y 10x^4y

(There is 2 missing fraction lines)

Answer 1

`(3y^(4))/(5x)\textrm{ or }(3)/(5)x^(-1)y^(4)`

Explanation:

The expression is:

`(2x^(3)y^(6))/(5x^(2)y)* (15x^(2))/(10x^(4)y)`

First, we will multiply the numerators together and denominators together.

This gives,

`((2* 15)(x^(3)* x^(2))(y^(6)))/((5* 10)(x^(2)* x^(4))(y* y))`

Now, we use the exponent property
`x^(a)* x^(b)=x^(a+b)`.

This gives,

`(30x^(3+2)y^(6))/(50x^(2+4)y^(2))\\=(30x^(5)y^(6))/(50x^(6)y^(2))`

Now, we use the exponent property
`(x^(a))/(x^(b))=x^(a-b)`

This gives,

`(30x^(5)y^(6))/(50x^(6)y^(2))=(3)/(5)x^(5-6)y^(6-2)=(3)/(5)x^(-1)y^(4)`

From the properties of exponents,
`x^(-a)=(1)/(x^(a))`

So,
`(3)/(5)x^(-1)y^(4)=(3y^(4))/(5x)`