Laws of Exponents Prepared by: Ruby Rose Concepcion III- B Math

Law I x¹ = x for all rational numbers

Law 2 [ Multiplication Law of Exponents] If we multiply two numbers with the same base, we add the exponents. The base remains the same.

Example : Multiply 2 ⁴ ∙ 2 ⁷ Solution: Method 2 2 ⁴ ∙ 2 ⁷ =(2 ∙ 2 ∙ 2 ∙ 2)(2 ∙2 ∙ 2 ∙ 2 ∙ 2 ∙ 2 ∙ 2) = 2¹¹ = 2048 Method 1 2 ⁴ ∙ 2 ⁷ = 16 ∙ 128 = 2048

Law 3 [ Power to a Power Law ] To raise a power to another, multiply the exponents.

Example :

Law 4 [ The Power of a Product Law ] Exponentiation distributes over multiplication

Example :

Law 5 [ The Division Law of Exponents] If we divide two numbers of the same base, we subtract the exponents and leave the same base.

Example : = = ·

Law 6 [ The Distributive Law of Exponents over Division ] An exponent distributes over division.

Example :