Question

What is the product of (3y^-4) (2y^-4) A. 6/y^8 B. 1/6y^8 C. 6/y^16 D. 1/6y^16

Answer 1

A

Explanation:

We want to simplify the product
`(3y^(-4))(2y^(-4))`.

First, notice that both terms have a power with base y, so by the properties of exponents, we can combine the two
`y^(-4)` into one by adding their exponents:

`y^(-4)*y^(-4)=y^(-4+(-4))=y^(-8)`

Now, let's multiply the 3 and 2:

3 * 2 = 6

So far, we have
`6y^(-8)`. However, we have a negative exponent that we want to make positive. Remember another property of exponents that when we have a negative exponent, we can make it positive by taking the reciprocal of it. Thus,
`y^(-8)` becomes
`(1)/(y^8)`.

Hence, our answer is
`6*(1)/(y^8)=(6)/(y^8)`, or A.

~ an aesthetics lover