Question 779425
<pre>
{{{log(a,(32))}}}{{{""+""}}}{{{expr(4/5)log(a,(16))}}}{{{""-""}}}{{{expr(4/5)log(a,(8))}}}{{{""+""}}}{{{log(a,(1/(2^"9/5")))}}}

Write the last term with a negative exponent

{{{matrix(2,1,"",log(a,(32)))}}}{{{matrix(2,1,"",""+"")}}}{{{matrix(2,1,"",expr(4/5)log(a,(16)))}}}{{{matrix(2,1,"",""-"")}}}{{{matrix(2,1,"",expr(4/5)log(a,(8)))}}}{{{matrix(2,1,"",""+"")}}}{{{matrix(2,1,"",log(a,(2^(-9/5)))))}}}

Write 32 as 2<sup>5</sup>, 16 as 2<sup>4</sup>, and 8 as 2<sup>3</sup>

{{{matrix(2,1,"",log(a,(2^5)))}}}{{{matrix(2,1,"",""+"")}}}{{{matrix(2,1,"",expr(4/5)log(a,(2^4)))}}}{{{matrix(2,1,"",""-"")}}}{{{matrix(2,1,"",expr(4/5)log(a,(2^3)))}}}{{{matrix(2,1,"",""+"")}}}{{{matrix(2,1,"",log(a,(2^(-9/5)))))}}}

Move the xponents out front as multipliers:

{{{5*log(a,(2))}}}{{{""+""}}}{{{4*expr(4/5)*log(a,(2))}}}{{{""-""}}}{{{3*expr(4/5)*log(a,(2))}}}{{{""+""}}}{{{(expr(-9/5))*log(a,(2))}}}

Simplify:

{{{5*log(a,(2))}}}{{{""+""}}}{{{expr(16/5)*log(a,(2))}}}{{{""-""}}}{{{expr(12/5)*log(a,(2))}}}{{{""-""}}}{{{expr(9/5)*log(a,(2))}}}

Factor out log<sub>a</sub>(2)

(5+{{{16/5}}}-{{{12/5}}}-{{{9/5}}})log<sub>a</sub>(2)

Write 5 as {{{25/5}}}

({{{25/5}}}+{{{16/5}}}-{{{12/5}}}-{{{9/5}}})log<sub>a</sub>(2)

{{{20/5}}}·log<sub>a</sub>(2)

4·log<sub>a</sub>(2)

Edwin</pre>