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Which of the following number sentences must be true? Indicate all suc
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10 Mar 2022, 03:00
10 Mar 2022, 03:00
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Which of the following number sentences must be true?
Indicate all such sentences.
(A) \(9^4 · 9^3 = 9^7\)
(B) \(2^2 · 3^3 = 6^5\)
(C) \(5^4 · 5^2 = 5^8\)
(D) \(10^4 · 10 = 10^5\)
(E) \(2^2 · 3^3 = 6^6\)
(F) \((2^3)^4 = 2^{12}\)
Indicate all such sentences.
(A) \(9^4 · 9^3 = 9^7\)
(B) \(2^2 · 3^3 = 6^5\)
(C) \(5^4 · 5^2 = 5^8\)
(D) \(10^4 · 10 = 10^5\)
(E) \(2^2 · 3^3 = 6^6\)
(F) \((2^3)^4 = 2^{12}\)
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Re: Which of the following number sentences must be true? Indicate all suc
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24 Mar 2022, 22:05
24 Mar 2022, 22:05
Carcass wrote:
Which of the following number sentences must be true?
Indicate all such sentences.
(A) \(9^4 · 9^3 = 9^7\)
(B) \(2^2 · 3^3 = 6^5\)
(C) \(5^4 · 5^2 = 5^8\)
(D) \(10^4 · 10 = 10^5\)
(E) \(2^2 · 3^3 = 6^6\)
(F) \((2^3)^4 = 2^{12}\)
Indicate all such sentences.
(A) \(9^4 · 9^3 = 9^7\)
(B) \(2^2 · 3^3 = 6^5\)
(C) \(5^4 · 5^2 = 5^8\)
(D) \(10^4 · 10 = 10^5\)
(E) \(2^2 · 3^3 = 6^6\)
(F) \((2^3)^4 = 2^{12}\)
Prperties to use;
\((x^a)(x^b) = x^{a+b}\)
\((x^a)(y^a) = (xy)^a\)
\((x^a)^b = x^{ab}\)
(A) \(9^4 · 9^3 = 9^7\) - YES
\(9^4 · 9^3 = 9^{4+3} = 9^7\)
(B) \(2^2 · 3^3 = 6^5\) - NO
\(2^2 · 3^3 = 2^2 · 3^2 . 3 = (2 . 3)^2 . 3 = 3 . 6^2 ≠ 6^5\)
(C) \(5^4 · 5^2 = 5^8\) - NO
\(5^4 · 5^2 = 5^{4+2} = 5^6 ≠ 5^8\)
(D) \(10^4 · 10 = 10^5\) - YES
\(10^4 · 10 = 10^{4+1} = 10^5\)
(E) \(2^2 · 3^3 = 6^6\) - NO
\(2^2 · 3^3 = 2^2 · 3^2 . 3 = (2 . 3)^2 . 3 = 3 . 6^2 ≠ 6^6\)
(F) \((2^3)^4 = 2^{12}\) - YES
\((2^3)^4 = 2^{3 . 4} = 2^{12}\)
Hence, option A, D and F
gmatclubot
Re: Which of the following number sentences must be true? Indicate all suc [#permalink]
24 Mar 2022, 22:05
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