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what is the value of a + b + c?
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25 Aug 2018, 15:16
25 Aug 2018, 15:16
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Question Stats:
87% (00:42) correct
12% (01:24) wrong based on 54 sessions
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If \(\frac{5^7}{5^{-4}}=5^a\), \(\frac{2^{-3}}{2^{-2}}=2^b\), and \(3^8(3) = 3^c\), what is the value of \(a + b + c\)?
Show: :: OA
19
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Re: what is the value of a + b + c?
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13 Dec 2018, 07:01
13 Dec 2018, 07:01
1
sandy wrote:
If \(\frac{5^7}{5^{-4}}=5^a\), \(\frac{2^{-3}}{2^{-2}}=2^b\), and \(3^8(3) = 3^c\), what is the value of \(a + b + c\)?
Show: :: OA
19
GIVEN: \(\frac{5^7}{5^{-4}}=5^a\)
Apply Quotient Law to get: \(5^{11}=5^a\)
So, a = 11
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GIVEN: \(\frac{2^{-3}}{2^{-2}}=2^b\)
Apply Quotient Law to get: \(2^{-1}=2^b\)
So, b = -1
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GIVEN: \(3^8(3) = 3^c\)
Rewrite as: \((3^8)(3^1) = 3^c\)
Apply Product Law to get: \(3^9 = 3^c\)
So, c = 9
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a + b + c = 11 + (-1) + 9 = 19
Answer: 19
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what is the value of a + b + c?
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21 Feb 2024, 22:16
21 Feb 2024, 22:16
1
\(\frac{5^7}{5^{-4}}= 5^7 \times 5^4 = 5^{7+4} = 5^{11} = 5^a, \text{ therefore } a = 11\)
\(\frac{2^{-3}}{2^{-2}} = 2^{-3} \times 2^2 = 2^{(-3+2)} = 2^{-1} = 2^b, \text{ therefore } b = -1\)
\(3^8(3) = 3^8 \times 3^1 = 3^{8+1} =3^9 = 3^c, \text{ therefore } c = 9\)
\(a+b+c = 11-1+9 = 19\)
The answer is 19
\(\frac{2^{-3}}{2^{-2}} = 2^{-3} \times 2^2 = 2^{(-3+2)} = 2^{-1} = 2^b, \text{ therefore } b = -1\)
\(3^8(3) = 3^8 \times 3^1 = 3^{8+1} =3^9 = 3^c, \text{ therefore } c = 9\)
\(a+b+c = 11-1+9 = 19\)
The answer is 19
