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GRE Prep Club Legend  Joined: 07 Jun 2014
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GRE Math Challenge #85-Simplify 2^x + 2^x [#permalink]
Expert's post 00:00

Question Stats: 22% (00:12) correct 77% (00:18) wrong based on 18 sessions
$$2^x + 2^x$$

(A) $$2^{x+1}$$
(B) $$2^{x+2}$$
(C) $$2^{2x}$$
(D) $$4^{x}$$
(E) $$4^{2x}$$
[Reveal] Spoiler: OA

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Sandy
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Re: GRE Math Challenge #85-Simplify 2^x + 2^x [#permalink]
sandy wrote:
$$2^x + 2^x$$

(A) $$2^{x+1}$$
(B) $$2^{x+2}$$
(C) $$2^{2x}$$
(D) $$4^{x}$$
(E) $$4^{2x}$$

Here
$$2^x + 2^x$$ = $$2^{x+1}$$

This can also be proved

by taking x = 3

then $$2^3 + 2^3$$ =$$(2^3)$$ * $$2^1$$ = 16 i.e $$2^{3 + 1}$$
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Re: GRE Math Challenge #85-Simplify 2^x + 2^x [#permalink]
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Expert's post
sandy wrote:
$$2^x + 2^x$$

(A) $$2^{x+1}$$
(B) $$2^{x+2}$$
(C) $$2^{2x}$$
(D) $$4^{x}$$
(E) $$4^{2x}$$

We can combine the terms in the same way we combine any like terms.
For example, k + k = 2k
And w² + w² = 2(w²)
And 3q³ + 3q³ = 2(3q³) = 6q³

Likewise, 2^x + 2^x = (2)2^x
= (2^1)(2^x)
= 2^(x + 1) [after we apply the product law]

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Brent Hanneson – Creator of greenlighttestprep.com Sign up for our free GRE Question of the Day emails Re: GRE Math Challenge #85-Simplify 2^x + 2^x   [#permalink] 14 Dec 2017, 10:18
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