Define an integer exponent.

An integer exponent indicates how many times a number, called the base, is multiplied by itself.

In mathematics, an exponent is a small number written to the upper right of a base number. For example, in \(2^3\), 2 is the base and 3 is the exponent. This means you multiply 2 by itself three times: \(2 \times 2 \times 2 = 8\). Exponents are a shorthand way to express repeated multiplication, making calculations easier and more concise.

When the exponent is a positive integer, it tells you how many times to use the base in a multiplication. For instance, \(5^4\) means \(5 \times 5 \times 5 \times 5 = 625\). If the exponent is zero, any non-zero base raised to the power of zero is 1. For example, \(7^0 = 1\). This is a special rule in mathematics that helps maintain consistency in calculations.

Negative exponents indicate division rather than multiplication. For example, \(2^{-3}\) means \(1 / (2 \times 2 \times 2) = 1/8\). Essentially, a negative exponent tells you to take the reciprocal of the base raised to the corresponding positive exponent.

Understanding integer exponents is crucial because they appear in various areas of mathematics, including algebra, geometry, and even in real-world applications like calculating compound interest or analysing scientific data. By mastering exponents, you can simplify complex problems and make your calculations more efficient.