Question

How do you simplify `5x ^ { 2} y ^ { 3} \times 10x y ^ { 9}`?

Answer 1

`50x^3y^12`

Explanation:

First, you multiply `5 xx 10` to get `50`. Then you have to add the exponents. So for `x`, it would be `2 + 1` (there is an imaginary `1` exponent on the other `x`), which would make it `x^3`.

For y, you would do the same thing, `3 + 9 = 12`.

So, it would look like this.

`5x^2y^3 xx 10xy^9`

`= 5x^2y^3 xx 10x^1y^9`

`= 50x^2y^3 xx x^1y^9`

`= 50 x^2 xx x^1 xx y^3 xx y^9`-

This is grouping the terms, making it easier to add them. When you do this, just add the exponents.

`= 50 x^3y^12`

Answer 2

`5x^2y^3xx10xy^9=color(blue)(50x^3y^12`

Explanation:

Simplify:

`5x^2y^3xx10xy^9`

Multiply the coefficients.

`5xx6xxx^2y^3xy^9`

Simplify.

`50x^2y^3xy^9`

Combine similar variables.

`50x^(2)xy^3y^9`

Apply the product rule of exponents: `a^ma^n=a^(m+n)`. No exponent is understood to be `1`.

`50x^(2+1)y^(3+9)`

Simplify.

`50x^3y^12`