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goodyear2013
If \((4^x)(8^y)(16^{7x}) = (8^{4y})(32^x)(64^y)\) what is the value of x/y?

A. 3/5
B. 2/3
C. 3/4
D. 1
E. 4/3

Let’s simplify the given equation by expressing all the bases in terms of powers of 2:

(2^2x)(2^3y)(2^28x) = (2^12y)(2^5x)(2^6y)

2^(30x + 3y) = 2^(18y + 5x)

30x + 3y = 18y + 5x

25x = 15y

x/y = 15/25 = 3/5

Answer: A
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goodyear2013
If \((4^x)(8^y)(16^{7x}) = (8^{4y})(32^x)(64^y)\) what is the value of x/y?

A. 3/5
B. 2/3
C. 3/4
D. 1
E. 4/3

\((4^x)(8^y)(16^{7x}) = (8^{4y})(32^x)(64^y)\)

Or, \((2^{2x})(2^{3y})(2^{28x}) = (2^{12y})(2^{5x})(2^{6y})\)

Or, \(2^{30x + 3y} = 2^{5x + 18y}\)

Or, \(25x = 15y\)

Or, \(5x = 3y\)

So, \(\frac{x}{y}= \frac{3}{5}\)

Thus, the correct answer will be (A)...
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