If a=(2^3)(4^3)(5^9) and b=(4^6)(5^6)(6^9), then which of

Question

If a=(2^3)(4^3)(5^9) and b=(4^6)(5^6)(6^9), then which of the following values is less than (ab)^1/3?

a. (2^7)(5^5)(6^3)
b. (2)(4^3)(5^5)(6^3)
c. (2^10)(3^3)(5^5)
d. (2^12)(5^5)(6)
e. (2^6)(5^3)(6^7)

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ywilfred · Answer

a = (2^3)(4^3)(5^9) = (2^3)(2^6)(5^9) = (2^9)(5^9) = (10^9)

b = (4^6)(5^6)(6^9) = (20^6)(6^9) = (20^6)(6^9)

ab = (20^6)(60^9)

ab^1/3 = (20^2)(60^3) 
= (2^2)(10^2)(2^3)(3^3)(10^3) 
= (2^5)(10^5)(3^3) 
= (2^5)(2^5)(5^5)(3^3)
= (2^10)(5^5)(3^3) -------> Ans: C

MA · Answer

do we really need the information given in the question? not really because the lowest is the OA. the question could be rephrased as "which of the following is the lowest?"

by observation (without calculation), D seems the lowest.

humans · Answer

I thinks its D

The equation (ab)^1/3 = (2^10)(3^3)(5^5)

a. (2^7)(5^5)(6^3) = (2^10)(3^3)(5^5)----Same
b. (2)(4^3)(5^5)(6^3) = (2^10)(3^3)(5^5)----Same
c. (2^10)(3^3)(5^5) = (2^10)(3^3)(5^5)----Same
d. (2^12)(5^5)(6) = (2^13)(3)(5^5) ------------This is lower than (ab)^1/3 Hence the answer
e. (2^6)(5^3)(6^7) = (2^13)(3^7)(5^3)

ps_dahiya · Answer

D is the lowest.

c.  (2^10)(3^3)(5^5)  
d. (2^12)(5^5)(6) = 2^12 * 5^5 * 2 * 3 = (2^3/3^2) * (2^10 * 5^5 * 3^3) =  (8/9) * (2^10 * 5^5 * 3^3)

If a=(2^3)(4^3)(5^9) and b=(4^6)(5^6)(6^9), then which of

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