SOLUTION: What expression raised to the fourth power is 81x12y8z16?

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Question 75504: What expression raised to the fourth power is 81x12y8z16?
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Take the one-forth power of 81%2Ax%5E12%2Ay%5E8%2Az%5E16
.
When you do you can write this as:
.
%2881%2Ax%5E12%2Ay%5E8%2Az%5E16%29%5E%281%2F4%29
.
This can be "expanded" by raising each of the 4 factors to the 1%2F4 power to get:
.

.
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%2F4. When you do that you get:
.
%28x%5E12%29%5E%281%2F4%29+=+x%5E%2812%2A%281%2F4%29%29=+x%5E%2812%2F4%29+=+x%5E3
.
and
.
%28y%5E8%29%5E%281%2F4%29+=+y%5E%288%2A%281%2F4%29%29+=+y%5E%288%2F4%29+=+y%5E2
.
and, finally
.
%28z%5E16%29%5E%281%2F4%29+=+z%5E%2816%2A%281%2F4%29%29+%2B+z%5E%2816%2F4%29+=+z%5E4
.
When you multiply all four of these results together you get:
.
%2B3%2Ax%5E3%2Ay%5E2%2Az%5E4 and -3%2Ax%5E3%2Ay%5E2%2Az%5E4
.
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.