Question

what is the ans of a raise to m  ÷n

Answer 1

the attachment is the answer

an eg:

4 raise to 3÷2 = (√4)³
                     =  √4×√4×√4
                     = 2×2×2
                     = 8

Answer 2

$you\ can\ solve\ a^{ \frac{m}{n} } \ in\ two\ ways. \\ \\1.\ a^{ \frac{m}{n} }=(a^{m})^{ \frac{1}{n} }= \sqrt[n]{a^{m}}$

Here you first need to calculate a^m and them find the nth root.

$2.\ a^{ \frac{m}{n} }=(a^{ \frac{1}{n} })^{m}= (\sqrt[n]{a} )^{m}$

Here you first need to find the nth root of a and then find its mth power.

For example: 27^2/3

$1.\ 27^{ \frac{2}{3} }=(27^{ \frac{1}{3} })^{2}=3^{2}=9\ \ (first\ third\ root\ of\ 27\ is\ calculated.)$

$2.\ 27^{ \frac{2}{3} }=(27^{2})^{ \frac{1}{3} }=729^{ \frac{1}{3} }=9\ \ (first\ square\ of\ 27\ is\ calculated.)$