Question

How do you multiply `x^ { 2} y ^ { 4} \cdot x ^ { 5} y ^ { 12}`?

Answer 1

See the explanation below for how to multiply this expression:

Explanation:

First you can rearrange this expression as follows:

`x^2x^5y^4y^12`

Next we can use the following rule for exponents to multiply the `x` and `y` terms separately:

`color(red)(x^ax^b = x^(a+b))`

`x^2x^5y^4y^12 = x^(2+5)y^(4+12) =`

`x^7y^16`

Answer 2

The result is `x^7*y^16`

Explanation:

Since multiplication is commutative, you can change the order of the terms. Write it as

`x^2*x^5*y^4*y^12`

Now, combine the powers that have the same base (`x` or `y`) by adding the exponents:

`x^(2+5)*y^(4+12) = x^7*y^16`

That is the final result.

Here's why the "add the exponents" rule works:

`x^2*x^5` is the same as `(x*x)*(x*x*x*x*x)`, which is simply `x^7`