SOLUTION: ((a^2)(b)/9th root((a^3)(b^6)) can you help me solve this problem please. Thanks

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Question 273496: ((a^2)(b)/9th root((a^3)(b^6))
can you help me solve this problem please.
Thanks

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28a%5E2%29%28b%29%29%2Froot%289%2C+a%5E3b%5E6%29
In simplifying expressions like this, it is often helpful to replace radicals with fractional exponents. So this is where we'll start:
%28%28a%5E2%29%28b%29%29%2F%28a%5E3b%5E6%29%5E%281%2F9%29
Now we can start using our rules and properties of exponents. In the denominator we can use the property, %28pq%29%5Ez+=+p%5Ez%2Aq%5Ez:
%28%28a%5E2%29%28b%29%29%2F%28%28a%5E3%29%5E%281%2F9%29%28b%5E6%29%5E%281%2F9%29%29
Then we can use the power of a power rule (i.e. multiply the exponents):
%28%28a%5E2%29%28b%29%29%2F%28a%5E%283%2F9%29b%5E%286%2F9%29%29
Reducing the fractions we get:
%28%28a%5E2%29%28b%29%29%2F%28a%5E%281%2F3%29b%5E%282%2F3%29%29
Now we'll use the rule for exponents when dividing (i.e. subtract the exponents):
a%5E%282-1%2F3%29b%5E%281-2%2F3%29
To subtract the exponents we need the same denominators:
a%5E%286%2F3-1%2F3%29b%5E%283%2F3-2%2F3%29
which simplifies to:
a%5E%285%2F3%29b%5E%281%2F3%29
which may be an acceptable answer. But we could also do the following:
%28a%5E5%2Ab%29%5E%281%2F3%29
root%283%2C+a%5E5b%29
root%283%2C+a%5E3%2Aa%5E2b%29
root%283%2C+a%5E3%29%2Aroot%283%2C+a%5E2b%29
a%2Aroot%283%2C+a%5E2b%29