document.write( "Question 633999: Can you simplify this radical: square root(sixth root(x^5 y^6 )) \n" ); document.write( "

Algebra.Com's Answer #399333 by jsmallt9(3759) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"sqrt%28root%286%2C+x%5E5y%5E6%29%29\"$
\n" ); document.write( "The easiest way to work with an expression which has multiple type of roots is to rewrite the radicals using fractional exponents.

\n" ); document.write( "A square root is the same as an exponent of 1/2 and a sixth root is the same as an exponent of 1/6. Rewriting your expression with these exponents instead of the radicals we get:
\n" ); document.write( " $\"%28%28x%5E5y%5E6%29%5E%28%281%2F6%29%29%29%5E%28%281%2F2%29%29\"$
\n" ); document.write( "Then, with the rule for exponents for raising a power to a power (i.e. multiply the exponents), this simplifies to:
\n" ); document.write( " $\"%28x%5E5y%5E6%29%5E%28%281%2F12%29%29\"$
\n" ); document.write( "This may be an acceptable answer. But we can easily switch back to radical form. 1/12 as an exponent means 12th root:
\n" ); document.write( " $\"root%2812%2C+x%5E5y%5E6%29\"$ \n" ); document.write( "

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