Question

What is the product of -8x^7 and -2xy^3

Answer 1

`-8x^7(-2xy^3) = 16x^8y^3`

Explanation:

⭐Multiplication rules

• negative * negative = positive
• negative * positive = negative
• positive * positive = positive

⭐ Exponent multiplication rule

• 
  `a^n * a^m = a^(n+m)`

⭐ Multiplying two terms with variables

• multiply the coefficients (the numbers next to the variables) and the variables

We need to utilize these 3 key points (⭐) when multiplying to terms with variables.

First, let's multiply the coefficients:

-8 * -2 = 16

• negative * negative = positive

Next, let's multiply the variables:

`x^7 * xy^3`

These two variables have the same base (x), so we will add their exponents up.

* remember: if you see a variable without an exponent, it has an exponent of 1 *

`x^7 * x = x^8`

• 
  `a^n * a^m = a^(n+m)`

The variable
`y^3` will stay the same because there is no other y variable.

=
`x^8y^3`

Now, "attach" the variables to the product of the coefficients:

=
`16x^8y^3`

Answer 2

16x^8y^3

Explanation:

Simplify the expression.