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655-705 (Hard)|   Exponents|      
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If 2a – 2−a = , what is the value of 4a + 4−a ? 08 Dec 2018, 07:37
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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)!

Difficulty:

55% (hard)

Question Stats:

64% (01:38) correct 36% (02:04) wrong based on 358 sessions

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If \(2^a – 2^{−a}\)= \(\sqrt{7}\) , what is the value of\(4^a + 4^{−a}\) ?


A. 1
B. 7
C. 9
D. 49
E. It cannot be determined from the information given.
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C
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If 2a – 2−a = , what is the value of 4a + 4−a ? 08 Dec 2018, 07:56
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Squaring \(2^a - 2^{-a}\) gives, \((2^a - 2^{-a})^2\) = \(4^a+4^{-a}-2*2^a*2^{-a}\)

\((\sqrt{7})^2\) = \(4^a+4^{-a}-2*2^a*2^{-a}\)

7 = \(4^a+4^{-a}-2*1\)

9 = \(4^a+4^{-a}\)

C is the answer.
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If 2a – 2−a = , what is the value of 4a + 4−a ? 08 Dec 2018, 08:04
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OA:C

\(2^a – 2^{−a}\)= \(\sqrt{7}\)

Squaring both sides, we get
\(2^{2a}+2^{−2a}-2*2^a*2^{-a}=7\)
\(4^a+4^{-a}-2=7\)
\(4^a+4^{-a}=9\)
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If 2a – 2−a = , what is the value of 4a + 4−a ? 08 Dec 2018, 08:06
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Scmfanatic
If \(2^a – 2^{−a}\)= \(\sqrt{7}\) , what is the value of\(4^a + 4^{−a}\) ?


A. 1
B. 7
C. 9
D. 49
E. It cannot be determined from the information given.
Show more

\(4^a + 4^{−a}\) = \(2^2a + 2^{−2a}\)

given,
\(2^a – 2^{−a}\)= \(\sqrt{7}\) ; squaring both sides
(a-b)^2 = a^2+b^2-2ab ; we get \(2^2a + 2^{−2a} - 2\) = 7
solving we get \(2^2a + 2^{−2a}\) = 9 C
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If 2a – 2−a = , what is the value of 4a + 4−a ? 08 Dec 2018, 08:08
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Important thing to note in this question is whenever you have a number and its reciprocal then remember that when ever you mutiply them would give you one. Also looking at the numbers you should note that (A + B)^2 = A^2 + B^2 + 2AB should do the trick in this question.

Option C is the correct answer.
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If 2a – 2−a = , what is the value of 4a + 4−a ? 05 Feb 2019, 20:27
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Afc0892
Squaring \(2^a - 2^{-a}\) gives, \((2^a - 2^{-a})^2\) = \(4^a+4^{-a}-2*2^a*2^{-a}\)

\((\sqrt{7})^2\) = \(4^a+4^{-a}-2*2^a*2^{-a}\)

7 = \(4^a+4^{-a}-2*1\)

9 = \(4^a+4^{-a}\)

C is the answer.
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Good night Afc0892 !

Would you be so kind and explain to me how do you go from 2^a*2^{-a} to *1?

Kind regards!
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Chethan92
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If 2a – 2−a = , what is the value of 4a + 4−a ? 05 Feb 2019, 21:01
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jfranciscocuencag
Afc0892
Squaring \(2^a - 2^{-a}\) gives, \((2^a - 2^{-a})^2\) = \(4^a+4^{-a}-2*2^a*2^{-a}\)

\((\sqrt{7})^2\) = \(4^a+4^{-a}-2*2^a*2^{-a}\)

7 = \(4^a+4^{-a}-2*1\)

9 = \(4^a+4^{-a}\)

C is the answer.

Good night Afc0892 !

Would you be so kind and explain to me how do you go from 2^a*2^{-a} to *1?

Kind regards!
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Hey jfranciscocuencag, sure :)

\(2^a*2^{-a}\) can be written as \(2^a*\frac{1}{2^a}\) then \(2^a\) will be cancelled out.

Hope it helps
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If 2a – 2−a = , what is the value of 4a + 4−a ? 07 Feb 2019, 19:44
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Scmfanatic
If \(2^a – 2^{−a}\)= \(\sqrt{7}\) , what is the value of\(4^a + 4^{−a}\) ?


A. 1
B. 7
C. 9
D. 49
E. It cannot be determined from the information given.
Show more

We can square both sides of the given equation and obtain:

(2^a - 2^(-a))^2 = (√7)^2

4^a + 4^(-a) - 2 = 7

4^a + 4^(-a) = 9

Answer: C
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If 2a – 2−a = , what is the value of 4a + 4−a ? 02 Jan 2025, 09:55
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Squaring 2a−2−a gives, (2a−2−a)^2 = 4a+4−a−2∗2a∗2−a

(√7)^2 = 4a+4−a−2∗2a∗2−a

7 = 4a+4−a−2∗1

9 = 4a+4−a

C is the answer.
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