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The law of exponents provides a set of rules for simplifying expressions involving powers, which represent repeated multiplication. These rules state that when multiplying powers with the same base, you add the exponents (\(a^{m}\times a^{n}=a^{m+n}\)); when dividing powers with the same base, you subtract the exponents (\(a^{m}/a^{n}=a^{m-n}\)); and when raising a power to another power, you multiply the exponents (\((a^{m})^{n}=a^{mn}\)). Common laws of exponents Product of powers: To multiply two numbers with the same base, add the exponents.Example: \(3^{2}\times 3^{3}=3^{2+3}=3^{5}\).Quotient of powers: To divide two numbers with the same base, subtract the exponents.Example: \(5^{4}/5^{2}=5^{4-2}=5^{2}\).Power of a power: To raise a power to another power, multiply the exponents.Example: \((7^{2})^{3}=7^{2\times 3}=7^{6}\).Zero exponent: Any non-zero base raised to the power of zero equals one.Example: \(10^{0}=1\).Negative exponent: A base raised to a negative exponent is equal to its reciprocal with a positive exponent.Example: \(x^{-n}=\frac{1}{x^{n}}\).Power of a product: To raise a product to a power, raise each factor to that power.Example: \((ab)^{n}=a^{n}b^{n}\).Power of a quotient: To raise a quotient to a power, raise both the numerator and the denominator to that power.Example: \((\frac{a}{b})^{n}=\frac{a^{n}}{b^{n}}\).