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01 Jul 2024, 01:30
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C
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Difficulty:
15%
(low)
Question Stats:
83% (01:12) correct
17%
(01:30)
wrong
based on 154
sessions
History
Date
Time
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Which of the following is equivalent to \(\frac{(\frac{1}{9})^{-9}(\frac{1}{27})^{-3}}{(\frac{1}{3})^{-27}}\)?
A. \(\frac{1}{3}\)
B. \(3^{-54}\)
C. \(1\)
D. \(3\)
E. \(3^{54}\)
A. \(\frac{1}{3}\)
B. \(3^{-54}\)
C. \(1\)
D. \(3\)
E. \(3^{54}\)
06 Jul 2024, 15:45
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Official Solution:
Which of the following is equivalent to \(\frac{(\frac{1}{9})^{-9}(\frac{1}{27})^{-3}}{(\frac{1}{3})^{-27}}\)?
A. \(\frac{1}{3}\)
B. \(3^{-54}\)
C. \(1\)
D. \(3\)
E. \(3^{54}\)
\(\frac{(\frac{1}{9})^{-9}(\frac{1}{27})^{-3}}{(\frac{1}{3})^{-27}}=\)
\(=\frac{(\frac{1}{3^2})^{-9}(\frac{1}{3^3})^{-3}}{(\frac{1}{3})^{-27}}=\)
\(=\frac{(\frac{1}{3})^{-18}(\frac{1}{3})^{-9}}{(\frac{1}{3})^{-27}}=\)
\(=(\frac{1}{3})^{-18}(\frac{1}{3})^{-9}(\frac{1}{3})^{27}=\)
\(=(\frac{1}{3})^{-18-9+27}=\)
\(=(\frac{1}{3})^{0}=\)
\(=1\)
Answer: C
Which of the following is equivalent to \(\frac{(\frac{1}{9})^{-9}(\frac{1}{27})^{-3}}{(\frac{1}{3})^{-27}}\)?
A. \(\frac{1}{3}\)
B. \(3^{-54}\)
C. \(1\)
D. \(3\)
E. \(3^{54}\)
\(\frac{(\frac{1}{9})^{-9}(\frac{1}{27})^{-3}}{(\frac{1}{3})^{-27}}=\)
\(=\frac{(\frac{1}{3^2})^{-9}(\frac{1}{3^3})^{-3}}{(\frac{1}{3})^{-27}}=\)
\(=\frac{(\frac{1}{3})^{-18}(\frac{1}{3})^{-9}}{(\frac{1}{3})^{-27}}=\)
\(=(\frac{1}{3})^{-18}(\frac{1}{3})^{-9}(\frac{1}{3})^{27}=\)
\(=(\frac{1}{3})^{-18-9+27}=\)
\(=(\frac{1}{3})^{0}=\)
\(=1\)
Answer: C
General Discussion
01 Jul 2024, 02:23
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\((1/9)^{-9}*(1/27)^{-3} / (1/3)^{-27}\)
=\(9^{9}*27^{3}/3^{27}\)
= \(3^{18}*3^{9}/3^{27}\)
= \(3^{27}/3^{27}\)
=1
=\(9^{9}*27^{3}/3^{27}\)
= \(3^{18}*3^{9}/3^{27}\)
= \(3^{27}/3^{27}\)
=1
