An exponent is a mathematical notation that indicates how many times a number, known as the base, is multiplied by itself. It is written as a small raised number to the right of the base. For example, in the expression \(2^3\):
- The base is \(2\).
- The exponent is \(3\).
This expression means \(2\) multiplied by itself \(3\) times:
\[ 2^3 = 2 \times 2 \times 2 = 8 \]
Exponents can also represent other concepts, such as roots. For instance, \(x^{1/n}\) represents the \(n\)th root of \(x\). Exponents can take on positive values, negative values (which represent the reciprocal, e.g., \(2^{-3} = 1/(2^3) = 1/8\)), and zero (where any non-zero base raised to the power of zero equals one).
In summary, exponents provide a concise way to express repeated multiplication and are foundational in various areas of mathematics, including algebra and calculus.
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