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81^3+27^4 is equivalent to which of the following expressio
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19 Jul 2019, 02:05
19 Jul 2019, 02:05
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Question Stats:
52% (00:45) correct
47% (01:12) wrong based on 44 sessions
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\(81^3+27^4\) is equivalent to which of the following expressions?
Indicate all such expressions.
A. \(3^7 \times 2\)
B. \(3^{12} \times 2\)
C. \(9^6 \times 2\)
D. \(9^{12}\)
E. \(3^{24}\)
Indicate all such expressions.
A. \(3^7 \times 2\)
B. \(3^{12} \times 2\)
C. \(9^6 \times 2\)
D. \(9^{12}\)
E. \(3^{24}\)
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Location: United States
GMAT 1: 770 Q51 V44
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WE:Education (Education)
Re: 81^3+27^4 is equivalent to which of the following expressio
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20 Jul 2019, 08:01
20 Jul 2019, 08:01
1
Expert Reply
Carcass wrote:
\(81^3+27^4\) is equivalent to which of the following expressions?
Indicate all such expressions.
A. \(3^7 \times 2\)
B. \(3^{12} \times 2\)
C. \(9^6 \times 2\)
D. \(9^{12}\)
E. \(3^{24}\)
Indicate all such expressions.
A. \(3^7 \times 2\)
B. \(3^{12} \times 2\)
C. \(9^6 \times 2\)
D. \(9^{12}\)
E. \(3^{24}\)
When manipulating exponents, begin by reducing to the least common base.
In this case, 81 and 27 can both be rewritten as bases of 3. 81 = 3⁴ and 27 = 3³.
Therefore, we can rewrite the given expression as (3⁴)³ + (3³)⁴.
Now, combine these exponent by multiplication to find that the expression is 3¹² + 3¹².
Finally, factor 3¹² from each term to get the final expression of 3¹²(1 + 1) or 3¹²(2) and select Choice B.
Eliminate Choices A, D, and E for including the wrong power of 3 and lacking the necessary multiple of 2.
However, reduce 9 in Choice C to a base of 3 to compare to the simplified expression.
9 = 3². So, rewrite the expression in Choice C as (3²)⁶ = 3¹²(2) proving that 9⁶(2) is equivalent to the simplified given expression and select Choice C as well.
The correct answers are Choices B and C.
gmatclubot
Re: 81^3+27^4 is equivalent to which of the following expressio [#permalink]
20 Jul 2019, 08:01
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