Exponents and Powers

Exponents
Exponents are a shorthand way of representing repeated multiplication of the same number. An exponent is represented as a small number written above and to the right of a base number. For example, in the expression 5^3, 5 is the base and 3 is the exponent. This means 5 is multiplied by itself three times.

Properties of Exponents:
- Multiplying Powers: When multiplying powers with the same base, you add the exponents. For example, (2^3) * (2^2) = 2^(3+2) = 2^5.
- Dividing Powers: When dividing powers with the same base, you subtract the exponents. For example, (3^4) / (3^2) = 3^(4-2) = 3^2.
- Power of a Power: When raising a power to another exponent, you multiply the exponents. For example, (4^2)^3 = 4^(2*3) = 4^6.

Powers
Powers are the result of raising a number to an exponent. The base number is raised to the power of the exponent to get the result. For example, in the expression 2^4, 2 is the base and 4 is the exponent, and the result is 16.

Relationship between Exponents and Powers:
- Exponents are used to represent how many times a number is multiplied by itself, while powers are the result of raising a number to an exponent.
- Exponents provide a compact way to write repeated multiplication, while powers show the final result of that multiplication.
- Understanding exponents and powers is essential in various mathematical operations, including simplifying expressions, solving equations, and working with scientific notation.