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a and b are real numbers with (-3xa)b = 81x12 for any value of x. What is the value of (-6a4b3)2 9ab3 (

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by Max@Math Revolution » Wed Jul 29, 2020 5:02 am
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[GMAT math practice question]

a and b are real numbers with (-3x^a)^b = 81x^12 for any value of x. What is the value of (-6a^4b^3)^2 \(\div\)9ab^3 \(\div\) (-2a^2)^2?

A. 1570
B. 1578
C. 1720
D. 1728
E. 1950
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Re: a and b are real numbers with (-3xa)b = 81x12 for any value of x. What is the value of (-6a4b3)2 9ab3 (

by Max@Math Revolution » Fri Jul 31, 2020 1:37 am
=>

Since (-3)^bx^ab = 3^4x^12, we have b = 4 and a = 3.
Then (-6a^4b^3)^2 ÷ 9ab^3 ÷(-2a^2)^2 = 36a^8b^6 ÷ 9ab^3 ÷ 4a^4 = a^3b^3 = 3^3·4^3 = 27·64 = 1728.

Therefore, D is the correct answer.
Answer: D
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