Question

why is 18^1/5 called the 5th root of 18?

Answer 1

by definition

Answer 2

\(\Large \bf a^{\frac{{\color{blue} n}}{{\color{red} m}}} = \sqrt[{\color{red} m}]{a^{\color{blue} n}}\qquad thus\quad 18^{\frac{{\color{blue}{ 1}}}{{\color{red}{ 5}}}}\implies ?\)

Answer 3

@satellite73 i dont understand what you mean by that..

Answer 4

there is no such thing as multiplying a number by itself one fifth time
we define
\[\huge b^{\frac{1}{n}}\] to be
\[\huge \sqrt[n]{b}\] in order to make the laws of exponents hold for fractional exponents as well as whole number exponents

Answer 5

one law of exponents is
\[\large (b^n)^m=b^{m\times n}\] that means if \(b^{\frac{1}{n}}\) is to make sense then since
\[\large (b^{\frac{1}{n}})^n=b^1=b\] making
\[\large b^{\frac{1}{n}}=\sqrt[n]{b}\]

Answer 6

oh got it thanks for the help @satellite73

Answer 7

yw