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(2^5+2^6+2^7+2^8)^2=?

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by Max@Math Revolution » Thu May 10, 2018 6:45 am
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[GMAT math practice question]

$$\left(2^5+2^6+2^7+2^8\right)^2=?$$

$$A.\ 2^83^25^2$$
$$B.\ 2^{10}3^45^4$$
$$C.\ 2^{10}+2^{12}+2^{14}+2^{16}$$
$$D.\ 2^{25}+2^{36}+2^{49}+2^{64}$$
$$D.\ 2^{10}3^25^2$$
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by GMATGuruNY » Thu May 10, 2018 8:03 am
Max@Math Revolution wrote:[GMAT math practice question]

$$\left(2^5+2^6+2^7+2^8\right)^2=?$$

$$A.\ 2^83^25^2$$
$$B.\ 2^{10}3^45^4$$
$$C.\ 2^{10}+2^{12}+2^{14}+2^{16}$$
$$D.\ 2^{25}+2^{36}+2^{49}+2^{64}$$
$$D.\ 2^{10}3^25^2$$
(2� + 2� + 2� + 2�)²

= [2�(1 + 2 + 2² + 2³)]²

= [2�(15)]²

= (2� * 3 * 5)²

= 2¹�3²5².

The correct answer is E.
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by Max@Math Revolution » Sun May 13, 2018 5:34 pm
=>



Therefore, E is the answer.
Answer : E
$$\left(2^5+2^6+2^7+2^8\right)^2$$
$$=\left(2^5\left(2^0+2^1+2^2+2^3\right)\right)^2$$
$$=\left(2^5\left(1+2+4+8\right)\right)^2$$
$$=\left(2^5\left(15\right)\right)^2$$
$$=\left(2^5\left(3\cdot5\right)\right)^2$$
$$=2^{10}\cdot3^2\cdot5^2$$

Therefore, E is the answer.
Answer : E
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by Jeff@TargetTestPrep » Tue May 15, 2018 3:44 pm
Max@Math Revolution wrote:[GMAT math practice question]

$$\left(2^5+2^6+2^7+2^8\right)^2=?$$

$$A.\ 2^83^25^2$$
$$B.\ 2^{10}3^45^4$$
$$C.\ 2^{10}+2^{12}+2^{14}+2^{16}$$
$$D.\ 2^{25}+2^{36}+2^{49}+2^{64}$$
$$D.\ 2^{10}3^25^2$$
From the expression in parentheses, we factor the common 2^5 and then simplify:

[2^5(1 + 2^1 + 2^2 + 2^3)]^2

2^10(1 + 2 + 4 + 8)^2

2^10(15)^2

2^10 x 5^2 x 3^2

Answer: E

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