Exponential Identities — Which identity is correct?

When multiplying, the exponents add; for power of a power, they multiply.

Exponents and Exponential Expressions

Exponentiation is a basic operation that indicates how many times a number is multiplied by itself. If a is a number and n is an integer, then aⁿ is the power.

Basic Identities

Negative and Fractional Exponents

The concept of exponents can be extended to negative and fractional exponents as well.

Negative exponent:
Fractional exponent:
In general:

Exponential Functions

Exponential functions are of the form where the variable is in the exponent. The most well-known is f(x) = a^x, where a > 0 and a ≠ 1.

If 0 < a < 1, the function is decreasing. If a > 1, it is increasing. This makes exponential functions extremely important in natural and social sciences.

Examples

Compound interest calculation:
Bacteria reproduction at an exponential rate.

Practice Exercise

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