SOLUTION: sqrt {a^-10b^-12}/sqrt {a^14d^-4}

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Question 442485: sqrt {a^-10b^-12}/sqrt {a^14d^-4}
Found 2 solutions by MathLover1, swincher4391:
Answer by MathLover1(20849) About Me  (Show Source):
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
To the first answerer:
Sorry, you are changing the problem by squaring the expression. So your final answer is not correct. If you were going to square everything, then you must remember to take the sqrt of your answer when you are done.
Another way we can write this is
sqrt%28a%5E-10%2Ab%5E-12%29+=+%28sqrt%28%28a%5E-5%29%5E2%2A%28b%5E-6%29%5E2%29%29%29
sqrt%28%28a%5E-5+%2Ab%5E-6%29%5E2%29
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sqrt%28a%5E14%2Ad%5E-4%29+=+%28sqrt%28%28a%5E7%29%5E2+%2A+%28d%5E-2%29%5E2%29%29%29
sqrt%28%28a%5E7+%2A+d%5E-2%29%5E2%29
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sqrt%28%28a%5E-5+%2A+b%5E-6%29%5E2%29+=+a%5E-5+%2A+b%5E-6
sqrt%28%28a%5E7+%2A+d%5E-2%29%5E2%29+=+a%5E7+%2A+d%5E-2
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So we have: %28a%5E-5+%2A+b%5E-6%29+%2F+%28a%5E7+%2A+d%5E-2%29
Since we are dividing, we subtract exponents of like bases:
%28a%5E%28-5-7%29+%2A+b%5E-6%29%2Fd%5E-2+=+%28a%5E%28-12%29+%2A+b%5E%28-6%29%29+%2F+d%5E-2
Negative exponents are not considered the simplest form. Negative exponent just means switch to either the numerator or denominator.
Thus our answer is: d%5E2+%2F+%28a%5E12+%2A+b%5E6%29