There are four important rules you must always remember when solving questions dealing with exponents.<\/p>\n
Rule One:<\/strong> When you multiply two exponents with the same base, add the exponents.<\/p>\n (x^3)(x^4) = x^(3+4) = x^7<\/p>\n (x^5)(x^3) = x^(5+3) = x^8<\/p>\n (3^2)(3^2) = 3^(2+2) = 3^(4) = 81<\/p>\n (2^2)(2^4) = 2^(2+4) = 2^6 = 64<\/p>\n Note: You cannot simplify (x^4)(y^3) because the bases are different.<\/p>\n <\/p>\n Rule Two:<\/strong> When you divide two exponents with the same base, subtract the exponents.<\/p>\n (x^4) \u00f7 (x^3) = x^(4-3) = x^1 = x<\/p>\n (x^5) \u00f7 (x^3) = x^(5-3) = x^2<\/p>\n (3^2) – (3^3) = 3^(2-3) = 3^(-1) = 1\/3<\/p>\n (2^2) \u00f7 (2^4) = 2^(2-4) = 2^(-2) = 1\/(2^2) = 1\/4<\/p>\n <\/p>\n Rule Three:<\/strong> When you have an exponent expression which is raised to a power, multiply the exponent and the power together.<\/p>\n (x^2)^4 = x^(2×4) = x^8<\/p>\n (3^2)^2 = 3^(2×2) = 3^4 = 81<\/p>\n (4^3)^2 = 4^(3×2) = 4^6 = 4096<\/p>\n (2^3)^5 = 2^(3×5) = 2^15<\/p>\n Notes:<\/strong><\/p>\n 1. If you have a product inside a set of brackets and a power outside of the brackets, then the power in applied to each element inside the brackets.<\/p>\n For example, (xy^2)^3 = x^(1×3)y^(2×3) = (x^3)(y^6).<\/p>\n 2. This rule does not work if you have a sum or a difference within the brackets. For example, (3+4)^2 is not equal to 3^2 + 4^2. Do not make this mistake! Exponents do not \u201cdistribute\u201d over addition or subtraction. Instead, we will have that (3+4)^2 = (3+4)(3+4) = (7)(7) = 7^2 = 49.<\/p>\n <\/p>\nExamples of Rule One:<\/h4>\n
Examples of Rule Two:<\/h4>\n
Examples of Rule Three:<\/h4>\n