Exponents — Chapter Summary

If a real number x

If a real number x is multiplied by itself n times, the expression is x^n. Here, x is the base and n is the exponent or power. For example, 2^25 means

When powers have the same base

When powers have the same base, multiplication adds the exponents: a^m × a^n = a^(m+n). For example, 3^3 × 3^5 = 3^8.

When powers with the same base

When powers with the same base are divided, the exponents are subtracted. If m>n, a^m / a^n = a^(m-n). If n>m, a^m / a^n = 1/a^(n-m).

When a power is raised

When a power is raised to another power, the exponents are multiplied: (a^m)^n = a^(mn). For example, (3^5)^2 = 3^10.

For any non

For any non-zero rational number a, a^-n = 1/a^n and a^n = 1/a^-n. Negative and positive powers are reciprocals of each other. For example, 5^-3 = 1/5