How do you simplify #(5/3)^ -3#?

Answer 1

#27/125#

#(5/3)^(-3)# First, distribute the -3 in the exponent to the numerator and the denominator. #((5^(-3))/(3^(-3)))# Because both of the exponents are negative the numerator and denominator have to switch. #((3^(3))/(5^(3)))# Simplify: #(27/125)#

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Answer 2

Julia Adams

#=(3/5)^3=27/125#

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Answer 3

Jace Anderson

To simplify ( \left(\frac{5}{3}\right)^{-3} ), you can take the reciprocal of ( \frac{5}{3} ) and raise it to the power of 3. So, ( \left(\frac{5}{3}\right)^{-3} = \left(\frac{3}{5}\right)^{3} ). Simplify the expression inside the parentheses and then raise it to the power of 3. ( \left(\frac{3}{5}\right)^{3} = \left(\frac{3^3}{5^3}\right) = \frac{27}{125} ). Therefore, ( \left(\frac{5}{3}\right)^{-3} = \frac{27}{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.