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Sub 505 (Easy)|   Exponents|      
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Bunuel
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(4^(-3) - 4^(-5))/4^(-5) = 01 Aug 2023, 09:00
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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5% (low)

Question Stats:

86% (00:59) correct 14% (01:13) wrong based on 511 sessions

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\(\frac{4^{-3} - 4^{-5}}{4^{-5}} = \)

A. 1/64
B. 1/15
C. 15
D. 16
E. 64
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C
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(4^(-3) - 4^(-5))/4^(-5) = 01 Aug 2023, 13:48
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Bunuel
\(\frac{4^{-3} - 4^{-5}}{4^{-5}} = \)

A. 1/64
B. 1/15
C. 15
D. 16
E. 64
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\(\frac{4^{-3} - 4^{-5}}{4^{-5}}\)

\(\frac{4^{-5} (4^2 - 1) }{4^{-5}}\)

Cancel \(4^{-5}\) from the numerator and from the denominator.

\(4^2 - 1\) = \(15\)

Option C
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(4^(-3) - 4^(-5))/4^(-5) = 06 Aug 2023, 15:08
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Bunuel
\(\frac{4^{-3} - 4^{-5}}{4^{-5}} = \)

A. 1/64
B. 1/15
C. 15
D. 16
E. 64
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(4ˉ³ - 4ˉ⁵)/4ˉ⁵ = 4ˉ³/4ˉ⁵ - 4ˉ⁵/4ˉ⁵ = 4² - 1 = 15

Answer: C
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raju1212
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(4^(-3) - 4^(-5))/4^(-5) = 01 Aug 2023, 09:58
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The numerator, will be \(\frac{1}{4^3}\) - \(\frac{1}{4}^5\) = \(\frac{ (4^5 - 4^3)}{4^8}\)

the denominator will be 1/4^5, take it up

\((4^5\) - \(4^3\)) * 4^5 / 4^8

= (4^5 - 4^3) / 4^3 | take common
= (4^2 - 1) * 4^3 / 4^3
= 4^2 -1
= 16-1
15

So the answer should be C.
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(4^(-3) - 4^(-5))/4^(-5) = 06 Aug 2023, 23:48
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(4ˉ³ - 4ˉ⁵)/4ˉ⁵
Multiply denominator and numerator by 4^5
=(4ˉ³ - 4ˉ⁵)*(4^5)/4ˉ⁵*(4^5)
=(4^2-1)/1
=16-1
=15

Hence C
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(4^(-3) - 4^(-5))/4^(-5) = 22 Feb 2024, 01:13
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Thanks for the solution!
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GmatKnightTutor
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(4^(-3) - 4^(-5))/4^(-5) = 22 Feb 2024, 12:40
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­Something that may help a bit is noticing that you could rewrite this as

\(\frac{a - b}{b}\)

a/b - b/b

a/b - 1

\(\frac{4^{-3}}{4^{-5}}\) - 1

Basically, you only need to figure out what 16 - 1 is… which is 15.

C is your answer.
 ­­­­
 
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(4^(-3) - 4^(-5))/4^(-5) = 13 May 2024, 05:52
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­Just multiply 4^5 through the numerator:

­
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(4^(-3) - 4^(-5))/4^(-5) = 05 Jul 2025, 12:29
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