Expert: Josh - 9/11/2008

Question
hi i need help with exponets i dont no if youll email me back but here's a problem i have (2x10)+ (8x10)+ (1x10)+ (1x10)
                           4 0s     2 0s    1 0s    0 0s
okay bi thanks

Answer
hi alyssa,

I tried to understand the question, but it has proved impossible because the characters no longer line up properly at the right places after you submit the question.

You can use the notation x^(y+2) to describe "x raised to the power of y+2", i.e., the "y+2" part is assumed to be written as superscript to the right of x.

Exponents refer to the part "y+2" in the explanation above.

e.g., 2^4 (read "two raised to the power of four") means you multiply 2 by itself 3 times. That is to say, 2^4 equals 2*2*2*2 = 16.

similarly, 5^3 means 5*5*5 and is equivalent to 125.

Now, if you ever have to multiply something like 2^3 and 2^2, just remember that the exponents add. Specifically, 2^3 * 2^2 = 2^(2+3) or 2^5.

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Rule 1: For any number x, with exponents a and b:
x^a * x^b = x^(a+b)
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You can verify this by expanding both sides of the equation
Left hand side: 2^3 * 2^2 = 2*2*2 * 2*2 = 8*4 = 32
Right hand side: we claim to be the same as 2^5, which expands as 2*2*2*2*2 and this is 32.

A slight modification of this theme is 2^3 / 2^2.
In this case, we subtract the second exponent from the first.

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Rule 1: For any number x, with exponents a and b:
x^a / x^b = x^(a-b)
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e.g., 2^3 / 2^2 should equal 2^(3-2) = 2^1 or 2.

Check to see this makes sense.
LHS: 2^3 / 2^2 = 8/4 = 2 as claimed.

Now, there are some definitions you need to remember.
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Rule 2: Any number raised to an exponent of 0 is by definition 1.
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e.g., 2^0 is 1, 6^0 is 1, 9732579^0 is also 1.

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Rule 3: Any number raised to one is just the number itself.
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e.g., 7^1 = 7.