Question 75504
Take the one-forth power of {{{81*x^12*y^8*z^16}}}
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When you do you can write this as:
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{{{(81*x^12*y^8*z^16)^(1/4)}}}
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This can be "expanded" by raising each of the 4 factors to the {{{1/4}}} power to get:
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{{{81^(1/4)*(x^12)^(1/4)*(y^8)^(1/4)*(z^16)^(1/4)}}}
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You can use a calculator (or you may be able to figure out) that the 4th root of 81 is 
either plus 3 or minus 3. For each of the other factors you can follow the power rule and 
multiply the exponent of the term by {{{1/4}}}.  When you do that you get:
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{{{(x^12)^(1/4) = x^(12*(1/4))= x^(12/4) = x^3}}}
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and 
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{{{(y^8)^(1/4) = y^(8*(1/4)) = y^(8/4) = y^2}}}
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and, finally
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{{{(z^16)^(1/4) = z^(16*(1/4)) + z^(16/4) = z^4}}}
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When you multiply all four of these results together you get:
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{{{+3*x^3*y^2*z^4}}} and {{{-3*x^3*y^2*z^4}}}
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and those two are the answers to the problem. You can check by multiplying both the answers
times themselves 4 times (four factors multiplied together) and see if you don't get back to 
the original expression.