document.write( "Question 610006: root13(root7(x)) = \n" ); document.write( "

Algebra.Com's Answer #384104 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"root%2813%2C+root%287%2C+x%29%29\"$
\n" ); document.write( "It is easier to see the answer if you replace the radicals with fractional exponents. A 7th root is equivalent to an exponent of 1/7:
\n" ); document.write( " $\"root%2813%2C+x%5E%281%2F7%29%29\"$
\n" ); document.write( "and a 13th root is equivalent to an exponent of 1/13:
\n" ); document.write( " $\"%28x%5E%281%2F7%29%29%5E%281%2F13%29\"$
\n" ); document.write( "The exponent rule for a power of a power is to multiply the exponents:
\n" ); document.write( " $\"x%5E%28%28%281%2F7%29%2A%281%2F13%29%29%29\"$
\n" ); document.write( " $\"x%5E%281%2F91%29\"$
\n" ); document.write( "Now we can revert back to radical form:
\n" ); document.write( " $\"root%2891%2C+x%29\"$ \n" ); document.write( "

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