How do you multiply u^ { - 1} v ^ { - 1} \cdot u v ^ { - 1} \cdot 3u ^ { 0}u−1v−1⋅uv−1⋅3u0?

1 Answer
Sally
Mar 8, 2017

3v^-23v−2 or 3/v^23v2.

Explanation:

You need to use exponent rules to multiply and simplify this expression.

Since all of the terms in the question are being multiplied, we can use the product rules for exponents. That is:

a^n * a^m = a^(n+m) an⋅am=an+m

Now, let's look at our expression:

u^-1v^-1uv^-1(3u^0)u−1v−1uv−1(3u0)

We can immediately simplify this by nothing that anything to the power of 00 is just one. So, we can turn the u^0u0 to 1. This leaves us with:

u^-1v^-1u^1v^-1(3)u−1v−1u1v−1(3)

The uu was written as u^1u1 to make the next step clearer.
Now, let's apply the product rule to terms with the same base.

u^-1v^-1u^1v^-1(3)u−1v−1u1v−1(3)
=u^(-1+1)v^(-1+ -1)(3)=u−1+1v−1+−1(3)
=u^0v^-2(3)=u0v−2(3)
=v^-2(3)=v−2(3)
=3v^-2=3v−2

This can also be written as 3/v^23v2 using the exponent rule a^-m=1/a^ma−m=1am.

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