document.write( "Question 74023: What expression raised to the fourth power is 81x12y8z16?
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Algebra.Com's Answer #53027 by bucky(2189)\"\" \"About 
You can put this solution on YOUR website!
Given: \"%2881%29%2A%28x%5E12%29%2A%28y%5E8%29%2A%28z%5E16%29\"
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\n" ); document.write( "To find the term that, when raised to the fourth power, results in the above expression,
\n" ); document.write( "you can just take the fourth root of the above expression. One way of writing the fourth root
\n" ); document.write( "is to just raise the above expression to the \"1%2F4\" power. Then you can use the rules
\n" ); document.write( "of exponents. When you raise the above to the \"1%2F4\" power, the expression becomes:
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\n" ); document.write( "\"%28%2881%29%2A%28x%5E12%29%2A%28y%5E8%29%2A%28z%5E16%29%29%5E%281%2F4%29\"
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\n" ); document.write( "next you apply the \"1%2F4\" power to each of the factors in the given expression to get:
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\n" ); document.write( "The first factor of 81 has a fourth root of 3 because 3*3*3*3 = 81. So let's replace \"81%5E%281%2F4%29\"
\n" ); document.write( "by 3. When you do the expression is simplified to:
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\n" ); document.write( "\"3%2A%28x%5E12%29%5E%281%2F4%29%2A%28y%5E8%29%5E%281%2F4%29%2A%28z%5E16%29%5E%281%2F4%29\"
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\n" ); document.write( "Then each of the other terms is raised to the \"1%2F4\" power by multiplying its exponent by \"1%2F4\".
\n" ); document.write( "So:
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\n" ); document.write( "\"%28x%5E12%29%5E%281%2F4%29+=+x%5E%2812%2F4%29+=+x%5E3\" and
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\n" ); document.write( "\"%28y%5E8%29%5E%281%2F4%29+=+y%5E%288%2F4%29+=+y%5E2\" and
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\n" ); document.write( "\"%28z%5E16%29%5E%281%2F4%29+=+z%5E%2816%2F4%29+=+z%5E4\"
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\n" ); document.write( "Multiplying all these answers together results in:
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\n" ); document.write( "\"3%2Ax%5E3%2Ay%5E2%2Az%5E4\"
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\n" ); document.write( "And that's the answer. If you reverse the process and raise the answer to the fourth
\n" ); document.write( "power, you get back to the original expression.
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\n" ); document.write( "Hope this helps you to see how the rules of exponents can be applied to a problem such
\n" ); document.write( "as this. You should be particularly aware that an exponent of \"1%2F2\" is equivalent
\n" ); document.write( "to taking the square root, and exponent of \"1%2F3\" is equivalent to taking the cube root,
\n" ); document.write( "and, as in this case, an exponent of \"1%2F4\" is equivalent to finding the fourth root ...
\n" ); document.write( "and so on. \n" ); document.write( "
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