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Actually, a base and exponent are not multiplied together. Rather, the exponent indicates the "power" of the base number, the number of times the base is to be multiplied by itself. For example the expression 23, where the base is 2 and the exponent is 3, represents the product of 3 2s; that is, 2 x 2 x 2, equaling 8. Powers of zero are a special case. By convention, and to support exponent operations, any number (excepting zero) to the power of zero equals one. Therefore the number with a base of 34 and exponent of 0 is written as 340, and 340 = 1.

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βˆ™ 2008-09-23 21:16:05
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A polynomial of degree zero is a constant term

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Q: How do you multiply a base of 34 and a exponent of 0?
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How can you tell if an exponential function is exponential growth or decay by looking at its base?

It is not enough to look at the base. This is because a^x is the same as (1/a)^-x : the key is therefore a combination of the base and the sign of the exponent.0 < base < 1, exponent < 0 : growth0 < base < 1, exponent > 0 : decaybase > 1, exponent < 0 : decaybase > 1, exponent > 0 : growth.

What is the base and exponent for 121?

You can choose the base to be any number (other than 0, -1 and 1) and calculate the appropriate exponent, or you can choose any exponent and calculate the appropriate base. For example, base 10: 121 = 10^2.08278537 (approx) Or exponent = 10: 121 = 1.615394266^10 (approx). I expect, though, that the answer that is required is 121 = 11^2.

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In exponential growth functions the base of the exponent must be greater than 1. How would the function change if the base of the exponent were 1 How would the function change if the base of the expon?

If the base of the exponent were 1, the function would remain constant. The graph would be a horizontal line. If the base of the exponent were less than 1, but greater than 0, the function would be decreasing.

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Take the exponent and multiply it by the coefficient (or 1 if there is no coefficient) then subract 1 from the exponent. For example, the derivative of 2x^3 is 6x^2 If there is no exponent, for example, 2x the derivative is 2 because the exponent is actually 1 which produces the same coefficient and the exponent 0 meaning there is no x.

What is the meaning of a zero exponent and the meaning of a negative exponent?

The zero exponent rule basically says that any base with an exponent of zero is equal to one. For example: x^0 = 1A negative exponent is equivalent to 1 over a positive exponent.x^1 = x x^0 = 1x^-1 = 1/x

Will a negative exponent on a positive base ever result to a number less than 0?

No, it cannot.

What does the term exponent mean in math?

Exponent means a little number in the upper corner of the number that indicates the number of times you multiply the base number (like in 3 to the 4th, 3 would be the base) times itself. 3 to the 4th means 3x3x3x3. 3 to the 4th equals 81. Oddly, any number to the power of 0 equals 1. Even 0 to the power of 0 equals one. That is what the term exponents means.

What is D x d x 20?

Dxdx^(20)Combine all similar variables in the expression.Dxdx^(20)=dDx^(21)To find the derivative of dx^(21)D, multiply the base (D) by the exponent (1), then subtract 1 from the exponent (1-1=0). Since the exponent is now 0, D is eliminated from the term.Dxdx^(20)=dx^(21)The derivative of Dxdx^(20) is dx^(21).dx^(21)

Is 0 to the power of 0 equals 0 a final answer?

Yes, 0 to the power of 0 equals 0 is a final answer.1. The law of exponentiationAll of the nth exponentiation of the same base ahas the same: a base constants.All of the exponentiation of any base a with the same exponent n has the same: n+1 exponent constants.All of the exponentiation an is analized and arranged unique by order and is equal to sums of meaning productsof:every base constant (from number 1, among abase constants, to the last number 1),withevery exponent constant (from number 1, among n+1 exponent constants, to the last number n!).2. The formula of exponentiation lawan =1&Atilde;&mdash;1 + (a-1)(2n-1) +&acirc;&euro;&brvbar;+ (a-1)&Atilde;&mdash;0,5[(n+1)!] + 1&Atilde;&mdash;n!3. 10000, 100, 20, 10, 00...?10000 According to the law:a=1000 has 1000 base constants (1, 999, ..., 999, 1),n=0 has 1 exponent constant (1), from there:10000=1&Atilde;&mdash;1+999&Atilde;&mdash;0=1+0=1&Acirc;&middot; 100 According to the law:a=10 has 10 base constants (1, 9, ..., 9, 1),n=0 has 1 exponent constant (1), from there:100=1&Atilde;&mdash;1+9&Atilde;&mdash;0=1+0=1&Acirc;&middot; 20 According to the law:a=2 has 2 base constants (1, 1), n=0 has 1 exponent constant (1), from there:20=1&Atilde;&mdash;1+1&Atilde;&mdash;0=1+0=1&Acirc;&middot; 10 According to the law:a=1 has 1 base constant (1), n=1 has 1 exponent constant (1) from there:10=1&Atilde;&mdash;1+0&Atilde;&mdash;0=1+0=1&Acirc;&middot; 00 According to the law:a=0 has 0 base constant (0), n=0 has 1 exponent constant (1), from there:00=0&Atilde;&mdash;1=000 = 0&Atilde;&mdash;1 = 0 is a final answer.00 = 1 is not a final answer..........................................................

Do negative exponent not mean to make the base number negative?

No, there is a big difference between 2^(-4) and (-2)^4 The first is 1/16 and the second is 16. A negative exponent is the reciprocal of a positive exponent. a^b is going to be 1/ (a^(-b)), Similarly, (a^b)*(a^(-b))=1 for two reasons. First multiplying reciprocals cancels them out. Second, when you multiply the same base you add the exponents, so (a^b)*(a^(-b)) = a^0 which equals 1&#9668;

12 with an exponent of 0?

120= 1 Anything with exponent 0 is 1, because if you multiply n0 by n0 you add the indices to get n0 and anything nonzero that when multiplied by itself gives itself, must be 1: if x2 = x then x2 - x = 0, so x(x-1)=0, so x=1 or 0.

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