Question 396715
{{{root(7,(8x^29)/(243x^8))}}}
<pre><font face = "batangche" color = "indigo" size = 4><b>

Don't split the radical up until you subtract the exponents of the x's

{{{root(7,(8x^21)/243)}}}

Now split it up:

{{{root(7,8x^21)/root(7,243)}}}

Since the power of x is a multiple of 7 we can take
it out of the radical on top, divide the exponent 21
by the index of the radical 7 and get x<sup>3</sup> which
we write in front of the top radical:

{{{x^3*root(7,8)/root(7,243)}}}

Since 243 = 3<sup>5</sup>, we replace 243 by that:

{{{x^3*root(7,8)/root(7,3^5)}}}

We have 3<sup>5</sup> on the bottom, and
we need 3<sup>7</sup> so that it will come out of the
radical, so we multiply by {{{red(  root(7,3^2)/root(7,3^2)  )}}}

{{{x^3*root(7,8)/root(7,3^5)}}}{{{""*""}}}{{{red(  root(7,3^2)/root(7,3^2)  )}}}

Multiply under the radicals:

{{{x^3*root(7,8*red(3^2))/root(7,3^5*red(3^2))}}}

{{{x^3*root(7,8*9)/root(7,3^7)}}}

Rewrite 8*9 as 72 and the denominator as just 3

{{{x^3*root(7,72)/3}}}



Edwin</pre></font></b>