Exponent Rules
Exponent rules are basic principles or formulas that govern the calculations involving exponents or powers of numbers
Exponent rules are basic principles or formulas that govern the calculations involving exponents or powers of numbers. These rules help simplify the manipulation of expressions and solve various mathematical problems. Let’s discuss some of the key exponent rules:
1. Product Rule: When multiplying two or more numbers with the same base, you keep the base and add the exponents.
Example: a^m * a^n = a^(m + n)
2. Quotient Rule: When dividing two numbers with the same base, you keep the base and subtract the exponents.
Example: a^m / a^n = a^(m – n)
3. Power Rule: To raise a power to another power, you multiply the exponents.
Example: (a^m)^n = a^(m * n)
4. Zero Exponent Rule: Any number (except zero) raised to the power of zero is equal to 1.
Example: a^0 = 1 (if a ≠ 0)
5. Negative Exponent Rule: To make a negative exponent positive, you can take the reciprocal of the base and change the sign of the exponent.
Example: a^(-n) = 1 / a^n
6. Product of Powers Rule: When multiplying numbers with the same exponent, you multiply the bases and keep the exponent.
Example: a^m * b^m = (a * b)^m
7. Quotient of Powers Rule: When dividing numbers with the same exponent, you divide the bases and keep the exponent.
Example: a^m / b^m = (a / b)^m
These rules are immensely useful in simplifying expressions, solving equations, and understanding the behavior of exponents in various mathematical operations. By applying these rules correctly, you can efficiently solve problems involving exponents.
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