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# If 5^7/5^(-4) = 5^a, 2^(-3)/2^(-2) = 2^b, and 3^8(3) = 3^c, what is

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Math Expert
Joined: 02 Sep 2009
Posts: 53004
If 5^7/5^(-4) = 5^a, 2^(-3)/2^(-2) = 2^b, and 3^8(3) = 3^c, what is  [#permalink]

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28 Jan 2019, 00:44
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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 $$a + b + c$$?

A. 18
B. 19
C. 20
D. 21
E. 22

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Re: If 5^7/5^(-4) = 5^a, 2^(-3)/2^(-2) = 2^b, and 3^8(3) = 3^c, what is  [#permalink]

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28 Jan 2019, 01:15
Bunuel 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 $$a + b + c$$?

A. 18
B. 19
C. 20
D. 21
E. 22

$$\frac{5^7}{5^{-4}}=5^a$$ => , a=11

$$\frac{2^{-3}}{2^{-2}}=2^b$$ =>, b=-1

$$3^8(3) = 3^c$$ => $$3^(8+1) = 3^c$$ => c=9

a+b+c =>11-1+9 = 19

Hence B
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VP
Joined: 31 Oct 2013
Posts: 1136
Concentration: Accounting, Finance
GPA: 3.68
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If 5^7/5^(-4) = 5^a, 2^(-3)/2^(-2) = 2^b, and 3^8(3) = 3^c, what is  [#permalink]

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28 Jan 2019, 01:25
Bunuel 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 $$a + b + c$$?

A. 18
B. 19
C. 20
D. 21
E. 22

$$\frac{5^7}{5^{-4}}=5^a$$

$$\frac{5^7*5^4=5^a$$

$$5^11 = 5^a$$

a = 11.

Again ,

$$[fraction]2^{-3}}{2^{-2}}=2^b$$

$$\frac{2^{2}}{2^{3}}=2^b$$

$$2^{-1} = 2^b$$

b = -1.

$$3^8(3) = 3^c$$

$$3^9 = 3^c$$

c = 9.

a + b + c = 11 + 9 -1 = 19.

The best answer is B.
VP
Joined: 09 Mar 2018
Posts: 1000
Location: India
If 5^7/5^(-4) = 5^a, 2^(-3)/2^(-2) = 2^b, and 3^8(3) = 3^c, what is  [#permalink]

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28 Jan 2019, 03:19
Bunuel 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 $$a + b + c$$?

A. 18
B. 19
C. 20
D. 21
E. 22

$$5^7 * 5^4 => 5^{11} = 5^a => a = 11$$

$$2^{-3 + 2} => 2^{-1} = 2^b => b = -1$$

$$3^9 => 9 = c$$

11 - 1 + 9

19

B
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Re: If 5^7/5^(-4) = 5^a, 2^(-3)/2^(-2) = 2^b, and 3^8(3) = 3^c, what is  [#permalink]

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28 Jan 2019, 03:48
Bunuel 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 $$a + b + c$$?

A. 18
B. 19
C. 20
D. 21
E. 22

solving we get
a= 11
b=-1
c=9
sum = 19
IMO B
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Re: If 5^7/5^(-4) = 5^a, 2^(-3)/2^(-2) = 2^b, and 3^8(3) = 3^c, what is   [#permalink] 28 Jan 2019, 03:48
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# If 5^7/5^(-4) = 5^a, 2^(-3)/2^(-2) = 2^b, and 3^8(3) = 3^c, what is

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