document.write( "Question 254531: use rational exponents to simplify: ^5√x^-30 \n" ); document.write( "

Algebra.Com's Answer #187410 by jsmallt9(3758) $\"\"$ $\"About$

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Assuming the problem is to simplify $\"root%285%2C+x%5E%28-30%29%29\"$ ...

\n" ); document.write( "Radicals can be rewritten as fractional exponents. 5th roots are exponents of 1/5. Replacing the radical with an exponent of 1/5 we get:
\n" ); document.write( " $\"%28x%5E%28-30%29%29%5E%281%2F5%29\"$
\n" ); document.write( "Now we can use the rule for exponents, $\"%28a%5Ep%29%5Eq+=+a%5E%28p%2Aq%29\"$ :
\n" ); document.write( " $\"x%5E%28-30%2A%281%2F5%29%29+=+x%5E%28-6%29\"$
\n" ); document.write( "So $\"x%5E%28-6%29\"$ is your answer unless you want positive exponents. With positive exponents it would be: $\"1%2Fx%5E6\"$ \n" ); document.write( "

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