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14 Oct 2016, 10:53
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Hi all -
So I'm a bit stuck with a relatively simple question. If the base of the two numbers is the same, but the variable exponent is different, what is the process to simply the equation?
For example: \(3^x+3\)^x+1
Obviously no hard and fast rules when it comes to addition and exponents, but any help would be appreciated.
So I'm a bit stuck with a relatively simple question. If the base of the two numbers is the same, but the variable exponent is different, what is the process to simply the equation?
For example: \(3^x+3\)^x+1
Obviously no hard and fast rules when it comes to addition and exponents, but any help would be appreciated.
14 Oct 2016, 16:10
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Jsur07
Hi all -
So I'm a bit stuck with a relatively simple question. If the base of the two numbers is the same, but the variable exponent is different, what is the process to simply the equation?
For example: \(3^x+3\)^x+1
Obviously no hard and fast rules when it comes to addition and exponents, but any help would be appreciated.
Dear Jsur07, So I'm a bit stuck with a relatively simple question. If the base of the two numbers is the same, but the variable exponent is different, what is the process to simply the equation?
For example: \(3^x+3\)^x+1
Obviously no hard and fast rules when it comes to addition and exponents, but any help would be appreciated.
I'm happy to respond.
This is not so much a "law of exponents" as a trick that involves some number sense.
You no doubt are familiar with the Distributive Law:
A*(B + C) = A*B + A*C
Technically, when we go from left to right in that equation, we are "distributing," and when we go from right to left, we are "factoring out."
We have to apply the factoring out process to the sum or difference of two different powers of the same base.
For example
\(3^x + 3^{x+1} = 1*(3^x) + 3*(3^x) = (1 + 3)*(3^x) = 4*(3^x)\)
We can use this trick even if the exponents are numbers instead of variables.
\(7^{30} + 7^{32} = 1*(7^{30}) + (7^2)*(7^{30}) = (1 + 49)*(7^{30}) = 50*(7^{30})\)
See this blog for more discussion of this technique:
Challenging GMAT Problems with Exponents and Roots
Does all this make sense?
Mike
17 Oct 2016, 13:59
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Check out this article covering that issue, as well as another interesting exponent 'trick': https://www.manhattanprep.com/gre/blog/ ... exponents/ It references the GRE, but the topic appears on the GMAT as well.
