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How do you simplify #9^-5#?

Answer 1

Avery Alexander

#1/9^5 " or " 1/59049 # which is less useful.

The negative index is the main issue.

This can be changed to #1/9^5#

#x^-1 = 1/x#

In my opinion this is the best form of the answer. We could simplify further to find the fraction #1/59049#

There isn't much benefit to using this form though; the index form is much more useful for using this fraction in calculations.

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Answer 2

Jameson Allen

To simplify (9^{-5}), you can use the property (a^{-n} = \frac{1}{a^n}).

(9^{-5} = \frac{1}{9^5} = \frac{1}{59049}).

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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.