How do you simplify #(125)^(-1/3)#?

Answer 1

#1/5#

There are two rules you'll need to know for this: #a^(1/m)=rootm(a)# #a^-m=1/a^m#

Now this question uses both of these rules to solve it: #125^-(1/3)=1/(125^(1/3))# #=1/root3(125)# And as your calculator or experience will tell you, #root3(125)# is 5; #=1/5#

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Answer 2

Isaiah Anthony

To simplify ( (125)^{-1/3} ), you can apply the negative exponent property, which states that ( a^{-n} = \frac{1}{a^n} ).

So, ( (125)^{-1/3} = \frac{1}{(125)^{1/3}} ).

Next, to find ( (125)^{1/3} ), you calculate the cube root of 125, which equals 5.

Therefore, ( (125)^{-1/3} = \frac{1}{5} ).

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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.