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How do you simplify #(9/2)^-1#?

Answer 1

Nathan Axel

See a solution process below:

There are a couple of ways we can do this. The first is to use these two rules of exponents:

#x^color(red)(a) = 1/x^color(red)(-a)# and #a^color(red)(1) = a#

#(9/2)^color(red)(-1) => 1/(9/2)^color(red)(- -1) => 1/(9/2)^color(red)(1) => 1/(9/2) => 2/9#

Another way is to use these rules of exponents:

#(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))# and #1/x^color(red)(a) = x^color(red)(-a)# and #x^color(red)(a) = 1/x^color(red)(-a)# and #a^color(red)(1) = a#

#(9/2)^color(red)(-1) => 9^color(red)(-1)/2^color(red)(-1) => 9^color(red)(-1) xx 1/2^color(red)(-1) => 1/9^color(red)(- -1) xx 2^color(red)(- -1) => 1/9^color(red)(1) xx 2^color(red)(1) => 1/9 xx 2 => 2/9#

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Answer 2

Abigail Allen

To simplify ( \left(\frac{9}{2}\right)^{-1} ), you reciprocate the fraction, which results in ( \frac{2}{9} ).

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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.