Question c9346

Nov 3, 2017

$3$

Explanation:

${27}^{\frac{1}{3}}$ can be written as ${\left({3}^{3}\right)}^{\frac{1}{3}}$.

When we have any function color(red)((a^b)^c, we multiply the exponents, thereforecolor(red)(a^(b*c)=a^(bc)#

So,

${27}^{\frac{1}{3}}$
$= {\left({3}^{3}\right)}^{\frac{1}{3}}$
$= {3}^{\textcolor{b l u e}{3 \cdot \frac{1}{3}}}$

We know that $\textcolor{b l u e}{\cancel{3} \cdot \frac{1}{\cancel{3}}} = 1$

So,

${3}^{\textcolor{b l u e}{3 \cdot \frac{1}{3}}}$
$= {3}^{1}$
$= 3$
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