I received this question on my CAT exam:
(3^5x + 3^5x + 3^5x) (4^5x + 4^5x + 4^5x + 4^5x) =
Answer: 12^5x+1
Please explain where the plus one in the answer comes from?
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- SarahWendee
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Re: CAT Exam
To be clear, the answer to this question is 12^(5x+1)
The first thing to do is to tidy up the first expression. Clearly 3^5x + 3^5x + 3^5x = 3(3^5x), and 4^5x + 4^5x + 4^5x + 4^5x = 4(4^5x).
Now, 3(3^5x) = 3^(5x+1). If this step is unclear, then consider that 2(2^4). You could write out 2(2^4) as 2x2x2x2x2, which equals 2^5.
So the expression in the question equals 3^(5x+1) x 4^(5x+1) = 12^(5x+1) (apologies for using x as both multiplication and a variable).
If this is still unclear, check out Exponents in the Algebra Strategy Guide for extra practice.
The first thing to do is to tidy up the first expression. Clearly 3^5x + 3^5x + 3^5x = 3(3^5x), and 4^5x + 4^5x + 4^5x + 4^5x = 4(4^5x).
Now, 3(3^5x) = 3^(5x+1). If this step is unclear, then consider that 2(2^4). You could write out 2(2^4) as 2x2x2x2x2, which equals 2^5.
So the expression in the question equals 3^(5x+1) x 4^(5x+1) = 12^(5x+1) (apologies for using x as both multiplication and a variable).
If this is still unclear, check out Exponents in the Algebra Strategy Guide for extra practice.
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