How do you rewrite #x^-5 x^5# using a positive exponent?

Answer 1

#x^0=1#.

Actually, #x^{-5}# is exactly the inverse number of #x^5#, assuming #x ne 0#. In fact, a negative power means "#1# over the positive power": #x^{-5}=1/{x^5}#.

So, #x^{-5}*x^5 = 1/{x^5}*x^5 = 1#

Obviously, #1=x^0# (any number to the power of zero is one, as long as the number is different from zero).

Also, using the power multiplication rule, we can work this way: you multiplicate powers of the same number by adding the exponents. In this case,

#x^{-5}*x^5=x^{-5+5}=x^0=1#.

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Answer 2

Eli Assouline

You rewrite (x^{-5} \cdot x^5) using a positive exponent as (x^{-5} \cdot x^5 = x^{-5 + 5} = x^0 = 1).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.