Question

What is the zero of the function represented by this graph

Answer 1

Answer: Choice D)  $g^{5/6}$

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Explanation:

The 6 is the index of the root, so we have a 6th root

We would use the rule $\sqrt[n]{x^m} = x^{m/n}$

Note how the index n moves to the denominator when we form the fraction m/n. The fraction m/n is the exponent.

So in this case, we can say,

$\sqrt[6]{g^5} = g^{5/6}$

which matches with choice D.

The requirement that g > 0 is to ensure that we don't have a negative under the square root. Applying the square root to a negative number leads to a complex number. If we want the result to be a real number, we need to have the stuff under the square root be 0 or positive.

Answer 2

The person above me is correct ^^