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

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XxxyyY
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If a=(2^3)(4^3)(5^9) and b=(4^6)(5^6)(6^9), then which of [#permalink] New post   13 Jul 2006, 17:32
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C
D
E

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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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Re: If a=(2^3)(4^3)(5^9) and b=(4^6)(5^6)(6^9), then which of [#permalink] New post   13 Jul 2006, 18:49
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
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Re: If a=(2^3)(4^3)(5^9) and b=(4^6)(5^6)(6^9), then which of [#permalink] New post   Updated on: 14 Jul 2006, 13:02
X & Y wrote:
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)


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.

Originally posted by MA on 13 Jul 2006, 20:41.
Last edited by MA on 14 Jul 2006, 13:02, edited 1 time in total.
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Re: If a=(2^3)(4^3)(5^9) and b=(4^6)(5^6)(6^9), then which of [#permalink] New post   13 Jul 2006, 22:22
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)
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Re: If a=(2^3)(4^3)(5^9) and b=(4^6)(5^6)(6^9), then which of [#permalink] New post   13 Jul 2006, 22:23
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)



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Re: If a=(2^3)(4^3)(5^9) and b=(4^6)(5^6)(6^9), then which of [#permalink]
13 Jul 2006, 22:23
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