Question 1145610
<pre>CORRECTED VERSION OF MY OTHER SOLUTION:

The first solution above is a decimal approximation using a calculator, 
and I'm sure your teacher would count that wrong.  Here is what your
teacher wants, which does not use a calculator:

{{{matrix(2,3,"","","",x^(3/4),""="",6)}}}

Raise both sides to the 4 power to cause the exponent
to be a whole number after we multiply:

{{{matrix(2,3,"","","",(x^(3/4))^4,""="",6^4)}}}

Multiply the exponents on the left to remove the parentheses
and make the exponent a whole number:

{{{matrix(2,3,"","","",x^3,""="",6^4)}}}

Take cube roots of both sides:

{{{matrix(2,3,"","","",root(3,x^3),""="",root(3,6^4))}}} 

On the left side, taking the cube root of a cube takes
away both the cube and the cube root!

On the right side, we break the 6<sup>4</sup> up as 6<sup>3</sup>6<sup>1</sup>
so we can take the cube root of part of the right side:

{{{matrix(2,3,"","","",x,""="",root(3,6^3*6))}}}

Since the cube root of a product is the product of the cube roots,
we take cube roots of both factors:

{{{matrix(2,3,"","","",x,""="",root(3,6^3)root(3,6))}}}

On the right side, we use the fact again that taking the cube root of 
a cube takes away both the cube and the cube root!:

{{{matrix(2,3,"","","",x,""="",6*root(3,6))}}}

Edwin</pre>