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# Which of the following is equivalent to 24^3*18^6/27^5?

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Re: Which of the following is equivalent to 24^3*18^6/27^5? [#permalink]
Bunuel wrote:
Which of the following is equivalent to $$\frac{24^3*18^6}{27^5}$$?

A. 2^14
B. 2^15
C. 2^16
D. 2^17
E. 2^18

Let’s simplify each term in our given expression:

24^3 = (2^3 x 3^1)^3 = 2^9 x 3^3

18^6 = (3^2 x 2^1)^6 = 3^12 x 2^6

27^5 = (3^3)^5 = 3^15

Thus, we have:

[(2^9 x 3^3) x (3^12 x 2^6)]/3^15

(2^15 x 3^15)/3^15

2^15