How do you simplify #-5^-3#?

Answer 1

#-5^-3=-1/125#

In the expression #-5^-3# there are 2 operations: power and multiplication by #(-1)#. According to the order of operations we have to calculate the power first remembering, that if the exponent is negative we have to write the expression as a positive power of the reciprocal of the base:

#(a/b)^-c=(b/a)^c#

So we get: #[-(1/5^3)]# Finally we can calculate the power #5^3# and write the final answer:

#-5^-3=-(1/5^3)=-1/125#

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Answer 2

Jace Anderson

To simplify -5^-3, first, find the reciprocal of 5^-3, which is (1/5)^3. Then, calculate (1/5)^3, which equals 1/(5^3). So, -5^-3 simplifies to -1/125.

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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.