document.write( "Question 253231: the fourth root of 49u^14..........simplify by first converting to rational expression..
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #185503 by drk(1908) $\"\"$ $\"About$

You can put this solution on YOUR website!
We start with fourth root (49*u^14).
\n" ); document.write( "We can rewrite this in fractional exponent form as
\n" ); document.write( "(i) $\"%2849u%5E14%29%5E%281%2F4%29\"$
\n" ); document.write( "Now, we are looking for groups of 4 in order to pull out one set. So I will expand (i) to get
\n" ); document.write( "(ii) $\"7%2A7%2Au%2Au%2Au%2Au%2Au%2Au%2Au%2Au%2Au%2Au%2Au%2Au%2Au%2Au\"$
\n" ); document.write( "Now I look for groups of four. I get
\n" ); document.write( "(iii) $\"7%2A7%2A%28u%2Au%2Au%2Au%29%2A%28u%2Au%2Au%2Au%29%2A%28u%2Au%2Au%2Au%29%2Au%2Au\"$
\n" ); document.write( "I see 3 groups of 4 u's, so I can take out the 3 groups as u^3. Nothing else comes out, so we are left with the answer as:
\n" ); document.write( "--
\n" ); document.write( " $\"u%5E3%2A%287%2A7%2Au%2Au%29%5E%281%2F4%29\"$
\n" ); document.write( "or
\n" ); document.write( " $\"u%5E3%2A%2849u%5E2%29%5E%281%2F4%29\"$ \n" ); document.write( "

\n" );