Algebra
Please Simplify:
(root5 a^7/2)^4 a^3/a^8
So confused, I tried figuring this out but need some help tracing the steps. I would appreciate some feedback! Thanks!

I have assumed that the fraction 7/2 is enclosed in parentheses, as follows:
(sqrt(5)*a^{(7/2)})^{4} a^{3}/a^{8}
Since the bases of the exponents are "a" or 5, you only have to apply the following rules of exponents to get your answer of 25a^{9}.
1. sqrt(5) = 5^{1/2}
2. distributive law:
(ab)^{x} = a^{x} b^{x}
3. addition of exponents of same base
a^{x} a^{y} = a^{x+y}
4. multiplication of exponents
(a^{x} )^{y} = a^{xy}
So:
(sqrt(5)*a^{(7/2)})^{4} a^{3}/a^{8}
=(sqrt(5)^{4}*(a^{(7/2)})^{4}) a^{38}
=25 a^{14} a^{5}
=25 a^{9}
posted by MathMate

WOW Thanks for the reply, but I still do not get how we get 25a^9. Can you please further explain. Thanks!
posted by Carmin

I get 25a^9/16? How can this be? Please help, still confused, thanks!
posted by Carmin

If you show your steps, it may help me spot where it has gone wrong.
posted by MathMate

...
=(sqrt(5)^{4}*(a^{(7/2)})^{4}) a^{38}
=5^{(1/2)*4}*a^{(7/2)*4}*a^{38}
=25 a^{14} a^{5}
=25 a^{9}
the denominator 2 in the fraction (7/2) is an exponent and not a simple number. This is probably from where you got the 16.posted by MathMate
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