- #1
Instinctlol
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This is a really basic problem and I just need some review.
How do I add 2k+1 + 2k+1?
This is where I am stuck
212k+212k
How do I add 2k+1 + 2k+1?
This is where I am stuck
212k+212k
eumyang said:Think of it this way. Can you add
x + x?
y + y?
something + something?
This is what the expression
2k+1 + 2k+1
merely is. Once you get that, then you can use the appropriate property of exponents.
Not only does it seem correct, it is correct.Instinctlol said:Oh I see, so it would be..
2*2k+1 = 2k+2
and just another one for fun
2k+1+2k+1+2k+1+2k+1 = 4*2k+1 = 2*2*2k+1 = 2k+3
Does this seem correct?
The basic rule for adding exponents is that when two numbers with the same base are being multiplied, the exponents can be added. For example, 23 + 24 = 27.
When the bases are not the same, the exponents cannot be added directly. In this case, the numbers can be rewritten as powers of the same base before adding the exponents. For example, 32 + 52 can be rewritten as (32)2 + (52)2 = 92 + 252 = 81 + 625 = 706.
Yes, exponents can be added in any order as long as the base and exponent pairs remain the same. For instance, 23 + 43 = 43 + 23 = 83.
When adding negative exponents, the same rules apply. If the bases are the same, the exponents can be added. If the bases are different, the numbers can be rewritten in terms of the same base before adding the exponents. For example, 2-3 + 2-4 = 2-7 and 3-2 + 5-2 = (3/5)2 + (5/3)2 = 9/25 + 25/9 = 2.04.
There are a few exceptions to the rule for adding exponents. One exception is when the base is raised to the power of 0. In this case, the result is always 1. Another exception is when the base is raised to the power of 1. In this case, the result is always the base itself. For example, 20 = 1 and 51 = 5.