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# confused with this exponents questions

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Intern
Joined: 23 Jul 2015
Posts: 26

Kudos [?]: 2 [0], given: 0

confused with this exponents questions [#permalink]

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19 Sep 2017, 13:08

If you work backwards...little bit confused how the first equations you only multiple the exponent with 2 (5x multiped by 2) and not the base (5 in base remains the same)

Again, working backwards in the bottom equations, but this time, you multiple the base by 2 (2 in base is multiplied by the exponent 2) but the exponent remains the same ($$\sqrt{y}$$ remains the same and is not multiped by 2.

Basically the question comes to... if you have a base and an exponent inside a parenthesis, raised to an exponent that is outside the parenthesis.... do you multiple the two exponents only (like the top left equation) or do you multiple the outside parenthesis exponent with the base inside the parenthesis only (like the bottom right equation)

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Intern
Joined: 26 Jul 2017
Posts: 18

Kudos [?]: 10 [0], given: 25

Location: India
Re: confused with this exponents questions [#permalink]

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19 Sep 2017, 16:08
jasonfodor wrote:

Basically the question comes to... if you have a base and an exponent inside a parenthesis, raised to an exponent that is outside the parenthesis.... do you multiple the two exponents only (like the top left equation) or do you multiple the outside parenthesis exponent with the base inside the parenthesis only (like the bottom right equation)

Both the issues that you have mentioned above, involves the use of this property:

a^mn = (a^m)^n

In the second equation that you have highlighted, this same property is being used its just that 4 is being written there as 2^2.

I would suggest you to go over the concepts of properties of exponents once.
Hope it helps!

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Manhattan Prep Instructor
Joined: 04 Dec 2015
Posts: 450

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GMAT 1: 790 Q51 V49
GRE 1: 340 Q170 V170
confused with this exponents questions [#permalink]

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19 Sep 2017, 16:28
jasonfodor wrote:

If you work backwards...little bit confused how the first equations you only multiple the exponent with 2 (5x multiped by 2) and not the base (5 in base remains the same)

Again, working backwards in the bottom equations, but this time, you multiple the base by 2 (2 in base is multiplied by the exponent 2) but the exponent remains the same ($$\sqrt{y}$$ remains the same and is not multiped by 2.

Basically the question comes to... if you have a base and an exponent inside a parenthesis, raised to an exponent that is outside the parenthesis.... do you multiple the two exponents only (like the top left equation) or do you multiple the outside parenthesis exponent with the base inside the parenthesis only (like the bottom right equation)

The reason for your confusion has to do with the specific numbers used in the problem. 4 equals 2^2, and 4 also equals 2*2. That isn't generally true: for instance, 9 = 3^2, but 9 doesn't equal 3*2.

In this case, you start with 4^something. Then you rewrite 4 as 2^2 (not 2*2). (2^2)^something = 2^(2*something). You always multiply the two exponents. You never multiply an exponent by a base; it only looks like that here because of the particular numbers they chose.
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Kudos [?]: 293 [0], given: 69

confused with this exponents questions   [#permalink] 19 Sep 2017, 16:28
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