document.write( "Question 389984: 8th root of (25a^2b^6) Use rational exponents to simplify expression. Answer in simplified radical form. \n" ); document.write( "

Algebra.Com's Answer #276938 by jsmallt9(3758) $\"\"$ $\"About$

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$\"root%288%2C+25a%5E2b%5E6%29\"$
\n" ); document.write( "There are no factors of $\"25a%5E2b%5E4\"$ that are powers of 8 so we cannot simplify this as it stands. Using a rational exponent for the 8th root we have:
\n" ); document.write( " $\"%2825a%5E2b%5E6%29%5E%281%2F8%29\"$
\n" ); document.write( "Since $\"25a%5E2b%5E4\"$ is a perfect square we can rewrite it as: $\"%285ab%5E2%29%5E2\"$ :
\n" ); document.write( " $\"%28%285ab%5E2%29%5E2%29%5E%281%2F8%29\"$
\n" ); document.write( "The rule for exponents when raising a power to a power is to multiply the exponents:
\n" ); document.write( " $\"%285ab%5E2%29%5E%282%2A%281%2F8%29%29\"$
\n" ); document.write( "which simplifies to:
\n" ); document.write( " $\"%285ab%5E2%29%5E%281%2F4%29\"$
\n" ); document.write( "We have simplified the expression as far as it can be simplified. Since we want the answer to be in radical form we rewrite an exponent as 1/4 as a 4th root:
\n" ); document.write( " $\"root%284%2C+5ab%5E2%29\"$ \n" ); document.write( "

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