The Basics: Evaluating X^N With Positive, Negative, And Fractional Exponents.

x^n

nx^n-1

The expression x^n represents x raised to the power of n. This means that x is multiplied by itself n number of times. For example, if x=2 and n=3, then x^n would be 2^3 which equals 8 (2 multiplied by itself 3 times).

If n is a positive integer, the value of x^n is always positive as long as x is not zero. If n is an even number, then the value of x^n will always be positive, even if x is negative. However, if n is an odd number, the value of x^n will depend on the sign of x. If x is positive, the value of x^n will be positive, but if x is negative, the value of x^n will be negative.

If n is a fraction or a decimal, then x^n is evaluated using logarithms. For example, if x=2 and n=1.5, then x^n would be calculated as 2^1.5 which can be written as 2^(3/2) in fractional form. This can be evaluated using logarithms as log(2^(3/2)) = (3/2)*log(2) which equals approximately 2.83.

In summary, x^n represents x raised to the power of n which means that x is multiplied by itself n number of times. The value of x^n depends on the sign of x when n is an odd number, and it is evaluated using logarithms when n is a fraction or a decimal.

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