SUPER HARD algebra 2 problem!!!?

LOL. I am on this exact point in my algebra 2 class. Anyway,

(15625 ^ 1/6 ) ^ 5

(5) ^ 5

3125 is the answer

When dealing with fractional exponents, it's usually easiest to break them up. you can break something like x^5/6 up into (x^5)^(1/6), because this implies that you will multiply the exponents together. Thus, you must raise the number to the fifth, then take the sixth route of the answer (raising something to a fraction is the same as routing it--raising to the one half would be taking the square route). unfortunately i don't have a calculator, but that's the method you should use.

15625 = [ (15625)^(1/6) ]^5 = 3125

3125

Its a partial fraction question! if you put the common denomiators in terms of linear factors you would get: x^2 - x - 6 = (x-3)(x+2) so really I can jump to: A(x + 2) + B(x - 3) = 2x - 9 Finding A let x = 3 therefore: 5A = -3 A = -3/5 Finding B let x = -2 -5B = -13 B = 13/5 I'll even prove that they work! -3/(5(x-3)) + 13/(5(x+2)) = [-3(x+2) + 13(x-3)]/[5(x-3)(x+2)] = [-3x - 6 + 13x - 39]/[5(x^2 - x - 6)] = 5(2x - 9)/5(x^2 - x - 6) = (2x - 9)/(x^2 - x - 6)

[ 15625^(1/6) ]^5

5^5

3,125

15625^(5/6)
= ±6√(15625^5) (±6√ = extract the sixth root of)
= ±6√(5^30)
= ±6√(5^5 * 5^5 * 5^5 * 5^5 * 5^5 * 5^5)
= ±5^5
= ±3125

That means take the 6th root of (15625 raised to the 5th power)


This can be done on a calculator with a y^x key, or since it has nice round numbers, you can also do this by using exponents:

15625=5^6
(5^6) ^(5/6)=5^(6*5/6)=5^5=3125