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Here are the Laws of Exponents explained in English: The Laws of Exponents are a set of rules that govern how to handle exponents in algebraic expressions. These rules simplify calculations and help in solving equations. Here are some fundamental rules: Product Rule: When multiplying powers with the same base, add the exponents. x^m · x^n = x^m+n Example: 2^3 · 2^4 = 2^3+4 = 2^7 Quotient Rule: When dividing powers with the same base, subtract the exponents. (x^m)/(x^n) = x^m-n Example: (5^6)/(5^2) = 5^6-2 = 5^4 Power of a Power Rule: When raising a power to another power, multiply the exponents. (x^m)^n = x^mn Example: (3^2)^3 = 3^2 · 3 = 3^6 Power of a Product Rule: When raising a product to a power, raise each factor to that power. (xy)^n = x^n y^n Example: (2 · 5)^3 = 2^3 · 5^3 Power of a Quotient Rule: When raising a quotient to a power, raise both the numerator and the denominator to that power. ((x)/(y))^n = (x^n)/(y^n) Example: ((4)/(7))^2 = (4^2)/(7^2) Zero Exponent Rule: Any non-zero number raised to the power of zero is 1. x^0 = 1 (where x ≠ 0) Example: 10^0 = 1 Negative Exponent Rule: A negative exponent means the reciprocal of the base raised to the positive exponent. x^-n = (1)/(x^n) Example: 4^-2 = (1)/(4^2) = (1)/(16) Fractional Exponent Rule: Fractional exponents represent roots. x^1/n = [n]x x^m/n = [n]x^m = ([n]x)^m Example: 9^1/2 = sqrt(9) = 3 Example: 8^2/3 = [3]8^2 = [3]64 = 4 What's next?