Fractional power

Question

By the definition of square root, we can take square root of $16$ as $\pm4$.

But in problems, why do we take $16^{\frac12}$ as $4$?

And also how can we say, if $a^m=b^n$ then $a=b^{m/n}$?

Because when we take $x^2=a$, we solve it as $x=\pm{a^{1/2}}$.

This site uses MathJax formatting of formulas. More tips here. (autocomment) — , Nov 15 '15 at 10:38
This question has been reiterated a lot of times here, see for instance here. — Workaholic, Nov 15 '15 at 10:42
I've fixed up your question a little bit, but it is still phrased in very low quality (there's only that much I can do). — barak manos, Nov 15 '15 at 10:42

score 0 · Answer 1 · answered Nov 15 '15 at 10:56

0

We take square root of 16 as 4 only when a negative solution is not viable e.g. when you are counting the number of objects, an answer of '-4' will not make any sense and is ignored.

answered Nov 15 '15 at 10:56

Amit Saxena

358

Fractional power

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