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Q: What is an irrational exponent?

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A number does not have an exponent in isolation. It has an exponent in the context of a base. The same number can have different combinations of base and exponent. For example, 64 = 8^2 or 4^3 or 2^6. A base cannot be zero but usually it is restricted to positive real numbers. In higher mathematics, the most common base is the irrational (even transcendental) number e = 2.71828...

The two are related. The answer could be base 2, exponent 18 or base 8, exponent 6 or base 10, exponent 5.4185 or base 262144, exponent 1 or base 68,719,476,736 and exponent 0.5

300 = 3 x 102

It is irrational.

Rational

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As many as you like. An exponent can be irrational and so have an infinite number of digits.

Rational, since it can be written as 25/1 .

A number does not have an exponent in isolation. It has an exponent in the context of a base. The same number can have different combinations of base and exponent. For example, 64 = 8^2 or 4^3 or 2^6. A base cannot be zero but usually it is restricted to positive real numbers. In higher mathematics, the most common base is the irrational (even transcendental) number e = 2.71828...

A number does not have an exponent in isolation. It has an exponent in the context of a base. The same number can have different combinations of base and exponent. For example, 64 = 8^2 or 4^3 or 2^6. A base cannot be zero but usually it is restricted to positive real numbers. In higher mathematics, the most common base is the irrational (even transcendental) number e = 2.71828...

A number does not have an exponent in isolation. It has an exponent in the context of a base. The same number can have different combinations of base and exponent. A base cannot be zero but usually it is restricted to positive real numbers. In higher mathematics, the most common base is the irrational (even transcendental) number e = 2.71828...Thus 105 = 105^1 or 10^2.0212 or e^4.6540

if there is no exponent shown, then the exponent is 1. ex: 41

A number does not have an exponent in isolation. It has an exponent in the context of a base. The same number can have different combinations of base and exponent. A base cannot be zero but usually it is restricted to positive real numbers. In higher mathematics, the most common base is the irrational (even transcendental) number e = 2.71828...Thus 216 = 216^1 or 10^2.3345 or e^5.3753 or 6^3 or 36^1.5 and so on.

An integer exponent is the number of times that a number is multiplied by itself. For example: if the exponent of a is 3, then it represents the number a3 = a*a*a. The laws of exponents can be extended to arrive at definitions of negative exponents [a-3 = 1/a3] and fractional exponents [a1/3 is the cube or third root of a]. These definitions can be further extended to exponents that are irrational numbers, or even complex number.

Yes, 25 CAN BE and exponent. Any number can be and exponent

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