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Which if the following equal (8)(72)^(-5)?

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Which if the following equal (8)(72)^(-5)?  [#permalink]

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New post 22 Nov 2019, 03:22
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

65% (01:39) correct 35% (01:56) wrong based on 55 sessions

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Re: Which if the following equal (8)(72)^(-5)?  [#permalink]

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New post 22 Nov 2019, 08:13
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Bunuel wrote:
Which if the following equal \((8)(72)^{-5}\)?

A. \(8^{-4}\)

B. \(8^{-5}\)

C. \(\frac{(72)^{-4}}{9}\)

D. \(\frac{(72)^{-5}}{8}\)

E. \(\frac{(72)^{-6}}{9}\)


Useful property: \((xy)^n = (x^n)(y^n)\)

Given: \((8)(72)^{-5}\)

Rewrite 72 as (8)(9) to get: \((8^1)(8^{-5})(9^{-5})\)

Simplify: \((8^{-4})(9^{-5})\)

Rewrite \(9^{-5}\) as follows: \((8^{-4})(9^{-4})(9^{-1})\)

Combine first two expressions: \((72^{-4})(9^{-1})\)

Rewrite \(9^{-1}\) as fraction to get: \((72^{-4})(\frac{1}{9})\)

Simplify: \(\frac{72^{-4}}{9}\)

Answer: C

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Brent
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Re: Which if the following equal (8)(72)^(-5)?  [#permalink]

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New post 04 Dec 2019, 06:00
(8)(72)^-5
8*(1/(72^5))......................Property x^-b=1/(x^b)
8*(1/((72)(72^4)).............. (72^5) can be written as (72)(72)(72)(72)(72) or (72)(72^4)
8/((72)(72^4))...................Resulting expression after multiplying what is in the parentheses by 8
1/((9)(72^4)).....................Canceling a factor of 8 from the numerator and the denominator
(72^-4)/9.......................... Property 1/(x^b)=x^-b (Reverse of what was listed in the first step)

Answer Choice C
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Re: Which if the following equal (8)(72)^(-5)?   [#permalink] 04 Dec 2019, 06:00
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