Exponenty

Exponenty is a mathematical concept that represents repeated multiplication. It is typically written in the form $a^n$, where 'a' is the base and 'n' is the exponent. The exponent 'n' indicates how many times the base 'a' should be multiplied by itself. For example, $2^3$ means 2 multiplied by itself three times, which is $2 \times 2 \times 2 = 8$. The result, 8, is called the power.

There are several rules associated with exponents. When multiplying numbers with the same base, you add their exponents: $a^m \times a^n = a^{m+n}$. For example, $2^2 \times 2^3 = 2^{2+3} = 2^5 = 32$. When dividing numbers with the same base, you subtract their exponents: $a^m / a^n = a^{m-n}$. For instance, $3^5 / 3^2 = 3^{5-2} = 3^3 = 27$. Raising a power to another power involves multiplying the exponents: $(a^m)^n = a^{m \times n}$. An example is $(4^2)^3 = 4^{2 \times 3} = 4^6$.

Any non-zero number raised to the power of zero is equal to 1: $a^0 = 1$. For example, $10^0 = 1$. A number raised to a negative exponent is equal to the reciprocal of the number raised to the positive exponent: $a^{-n} = 1/a^n$. For instance, $5^{-2} = 1/5^2 = 1/25$. Exponents are fundamental in various fields of mathematics, including algebra, calculus, and number theory, and have applications in science and engineering.