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How do you simplify #3^-2+2^-3#?

Answer 1

Ethan Adkins

#17/72#

Expression #= 3^-2 + 2^-3#

#= 1/3^2 + 1/2^3#

#= 1/9 + 1/8#

#= (8+9)/(9xx8)#

#= 17/72#

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Answer 2

Julia Adams

As,

#a^(-m)=1/(a^m)#

#3^(-2) + 2^(-3)#

#darrcolor(white)(dddd)darr#

#1/(3^2) color(white)(d)+ color(white)(d) 1/2^3#

As,

#3^2=9,2^3=8#

#1/9+1/8#

Now find the LCM.... it is 72

#(1xx8)/(9xx8)+(1xx9)/(8xx9)#

#8/72+9/72#

Add

#17/72#

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Answer 3

Eli Assouline

To simplify (3^{-2} + 2^{-3}):

(3^{-2} = \frac{1}{3^2} = \frac{1}{9})
(2^{-3} = \frac{1}{2^3} = \frac{1}{8})
Add the fractions together: (\frac{1}{9} + \frac{1}{8})
Find a common denominator, which is 72.
Rewrite each fraction with the common denominator: (\frac{8}{72} + \frac{9}{72})
Add the numerators: (\frac{8 + 9}{72} = \frac{17}{72})

So, (3^{-2} + 2^{-3}) simplifies to (\frac{17}{72}).

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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.