How do you multiply #u^ { - 1} v ^ { - 1} \cdot u v ^ { - 1} \cdot 3u ^ { 0}#?

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Answer 1 · 2017-03-08T10:44:51

#3v^-2# or #3/v^2#.

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) #

Now, let's look at our expression:

#u^-1v^-1uv^-1(3u^0)#

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

#u^-1v^-1u^1v^-1(3)#

The #u# was written as #u^1# 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^(-1+1)v^(-1+ -1)(3)#
#=u^0v^-2(3)#
#=v^-2(3)#
#=3v^-2#

This can also be written as #3/v^2# using the exponent rule #a^-m=1/a^m#.