How do you write #root3(125)# in exponential form?

Answer 1

#root3 125 = 125^(1/3)#

You need to be aware that roots can be written as indices (exponents). By definition, # rootn x = x^(1/n)" " eg. sqrtx = x^(1/2)#

This is then true for any root #rArr root3 x = x^(1/3)#

In this case #root3 125 = 125^(1/3)#

This is now written in the required form, but it can be simplified to give an answer of 5.

#root3 125 = root 3 5^3 = 5#

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Answer 2

Genesis Allen

To write (\sqrt[3]{125}) in exponential form, you express it as (125^\frac{1}{3}).

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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.