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

Oct 31, 2017

$50 {x}^{3} {y}^{12}$

#### Explanation:

First, you multiply $5 \times 10$ 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.

$5 {x}^{2} {y}^{3} \times 10 x {y}^{9}$

$= 5 {x}^{2} {y}^{3} \times 10 {x}^{1} {y}^{9}$

$= 50 {x}^{2} {y}^{3} \times {x}^{1} {y}^{9}$

$= 50 {x}^{2} \times {x}^{1} \times {y}^{3} \times {y}^{9}$-

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

$= 50 {x}^{3} {y}^{12}$

Oct 31, 2017

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

#### Explanation:

Simplify:

$5 {x}^{2} {y}^{3} \times 10 x {y}^{9}$

Multiply the coefficients.

$5 \times 6 \times {x}^{2} {y}^{3} x {y}^{9}$

Simplify.

$50 {x}^{2} {y}^{3} x {y}^{9}$

Combine similar variables.

$50 {x}^{2} x {y}^{3} {y}^{9}$

Apply the product rule of exponents: ${a}^{m} {a}^{n} = {a}^{m + n}$. No exponent is understood to be $1$.

$50 {x}^{2 + 1} {y}^{3 + 9}$

Simplify.

$50 {x}^{3} {y}^{12}$