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If x is a positive integer, and m = 1^(x+1), then what is the value of
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Author:  Bunuel [ 27 Jun 2022, 19:15 ]
Post subject:  If x is a positive integer, and m = 1^(x+1), then what is the value of

If x is a positive integer, and \(m=3^{x+1}\), then what is the value of \(9^{2x}\) in terms of m?


(A) \(\frac{m^2}{9}\)

(B) \(\frac{m^2}{81}\)

(C) \(\frac{m^3}{9}\)

(D) \(\frac{m^4}{3}\)

(E) \(\frac{m^4}{81}\)

Author:  Iotaa [ 27 Jun 2022, 20:50 ]
Post subject:  Re: If x is a positive integer, and m = 1^(x+1), then what is the value of

Bunuel wrote:
If x is a positive integer, and \(m=3^{x+1}\), then what is the value of \(9^{2x}\) in terms of m?


(A) \(\frac{m^2}{9}\)

(B) \(\frac{m^2}{81}\)

(C) \(\frac{m^3}{9}\)

(D) \(\frac{m^4}{3}\)

(E) \(\frac{m^4}{81}\)



\(m=3^{x+1}\);
\(Also, m=3^{x} *3\)

\(9^{2x} = 3^{4x} = 3^{x} X 3^{x} X 3^{x} X 3^{x}\)

\( Also, 3^{x}\) = m/3
=> \(3^{x} X 3^{x} X 3^{x} X 3^{x}\) = m/3 X m/3 X m/3 X m/3 = \(m^{4}/81\) , option E

Author:  Kinshook [ 27 Jun 2022, 21:24 ]
Post subject:  Re: If x is a positive integer, and m = 1^(x+1), then what is the value of

Asked: If x is a positive integer, and \(m=3^{x+1}\), then what is the value of \(9^{2x}\) in terms of m?

\(9ˆ{2x+2} = 81*9ˆ{2x} = 3ˆ{4x + 4} = mˆ4\)
\(9ˆ{2x} = \frac{mˆ4}{81} \)

IMO E

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