Laws of Exponents for Real Numbers

What are the Laws of Exponents?

The Laws of Exponents are a set of rules that describe how to manipulate expressions involving exponents.

What is the Law of Product of Powers?

The Law of Product of Powers states that when multiplying two powers with the same base, you add their exponents. For example, a^m × aⁿ = a^m+n.

What is the Law of Power of a Power?

The Law of Power of a Power states that when raising a power to another exponent, you multiply the exponents. For example, (a^m)ⁿ = a^mn.

What is the Law of Power of a Product?

The Law of Power of a Product states that when raising a product to a power, you can distribute the exponent to each term inside the parentheses. For example, (ab)ⁿ=aⁿ × bⁿ.

What is the Law of Quotient of Powers?

The Law of Quotient of Powers states that when dividing two powers with the same base, you subtract their exponents. For example, aⁿ/a^m​ = a^m−n.

What is the Law of Zero Exponent?

The Law of Zero Exponent states that any nonzero base raised to the power of zero is equal to 1. For example, a⁰ = 1.

What is the Law of Negative Exponent?

The Law of Negative Exponent states that any nonzero base raised to a negative exponent is equal to the reciprocal of the base raised to the positive exponent. For example, a⁻ⁿ = 1/aⁿ​.

Laws of Exponents are fundamental rules used in mathematics to simplify expressions involving exponents. These laws help in solving arithmetic problems efficiently by defining operations like multiplication, division, and more on exponents. In this article, we will discuss the laws of exponent for real number in detail with some solved examples.