Exponents and Powers: Fundamental Laws Quiz

Exponents and Powers

Exponents, also known as powers, refer to repeated multiplication of a number by itself. They can be expressed with notation like x^n, where 'x' is the base and 'n' indicates how many times it has been multiplied by itself. Exponents play a significant role in mathematics, particularly in algebra and calculus, because they allow us to simplify complex expressions and analyze patterns more easily.

The following sections will cover the fundamental laws of exponents, which help us understand and manipulate exponent expressions effectively. These laws ensure consistency when working with exponents and make calculations faster and easier by applying common sense principles.

Laws of Exponents

Product of Powers Rule

If n > m, then x^(m + n) = x^m * x^n = x^m × x^n = x^(m + n).

Power of a Power Rule

(x^m)^n = x^(m × n).

Quotient of Powers Rule

If n > m, then x^m ÷ x^n = x^(m - n).

Laws of Exponents for Exponents with Different Bases

If m and n are integers, and p is a positive real number, then:

1. x^m / y^m = (x / y)^m.
2. x^m × y^m = (xy)^m.

Laws of Exponents for Exponents with Different Bases

If m and n are integers, and p and q are positive real numbers, then:

1. x^m / y^m = (x / y)^m.
2. (x^m)^n = x^(m × n).

Laws of Exponents for Exponents with Different Bases

If m and n are integers, and p and q are positive real numbers, then:

1. (x^m)^(1/n) = x^(m/n).
2. x^m / y^(m - n) = x^m × y^(-n).