What does the exponent in an expression indicate?

The exponent in an expression indicates how many times the base is multiplied by itself. It is a shorthand notation that simplifies the representation of repeated multiplication. For example, in the expression \( a^n \): - \( a \) is the base. - \( n \) is the exponent. This means that \( a \) is multiplied by itself \( n \) times. Here are a few key points about exponents: 1. **Positive Exponents**: If \( n \) is a positive integer, \( a^n = a \times a \times a \times \ldots \) (n times). 2. **Zero Exponent**: Any non-zero number raised to the power of zero is equal to 1, i.e., \( a^0 = 1 \) (for \( a \neq 0 \)). 3. **Negative Exponents**: A negative exponent indicates the reciprocal of the base raised to the absolute value of the exponent, i.e., \( a^{-n} = \frac{1}{a^n} \). 4. **Fractional Exponents**: A fractional exponent indicates a root. For example, \( a^{\frac{1}{n}} \) represents the \( n \)-th root of \( a \). 5. **Properties of Exponents**: There are several important properties, such as: - \( a^m \times a^n = a^{m+n} \) - \( \frac{a^m}{a^n} = a^{m-n} \) - \( (a^m)^n = a^{m \cdot n} \) Understanding exponents is fundamental in algebra and is widely used in various mathematical contexts, including polynomials, exponential functions, and scientific notation.