SOLUTION: How would I find the radical expression of 4 over a^9

Question 463027: How would I find the radical expression of 4 over a^9

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
4/a^9 = 4*a^(-9)
this is because of the law of exponents that states that a^(-b) = 1/a^b.
4 * a^(-9) = 4 * 1/a^9 = 4/a^9.
not sure if this is what you want, but that's the equivalent expression.
if you are asking how to solve for a, you would do the following:
set the expression equal to some value which we'll call y.
you will get the equation y = 4/a^9
multiply both sides of this equation by a^9 and divide both sides of this equation by y to get a^9 = (4/y)
take the 9th root of both sides of this equation to get a = (4/y)^(1/9) which is equivalent to the expression
when you know the value of y, you can solve for a.
an example:
your expression is 4/a^9.
let y = 3000.
your equation is y = 4/a^9 which becomes 3000 = 4/a^9.
you solve for a to get a = (4/3000)^(1/9) which becomes a = .479235243
you confirm this by plugging that value for a in the original equation of 3000 = 4/a^9 which gets you 3000 = 4/(.479235243^9) = 4/.0013333333 = 3000, confirming the answer is good.

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