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

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Math Expert
Joined: 02 Sep 2009
Posts: 59721
Which if the following equal (8)(72)^(-5)?  [#permalink]

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22 Nov 2019, 03:22
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Difficulty:

45% (medium)

Question Stats:

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

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

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

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22 Nov 2019, 08:13
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Top Contributor
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: $$\frac{72^{-4}}{9}$$

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

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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)

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