Match the exponent law with the mathematical operation you do to the exponents: Quotient, Product, Power.
Understand the Problem
The question is asking to match different exponent laws with their corresponding mathematical operations related to exponents. The laws include Quotient, Product, and Power, and the task is to identify which operation applies to each law.
Answer
- Product of Powers: Multiplication of like bases - Quotient of Powers: Division of like bases - Power of a Power: Raising one exponent to another
Answer for screen readers
- Product of Powers: Multiplication of like bases
- Quotient of Powers: Division of like bases
- Power of a Power: Raising one exponent to another
Steps to Solve
- Identify the Laws of Exponents
Review the exponent laws you need to match:
- Product of Powers: $a^m \cdot a^n = a^{m+n}$
- Quotient of Powers: $\frac{a^m}{a^n} = a^{m-n}$
- Power of a Power: $(a^m)^n = a^{m \cdot n}$
- Classify the Operations
Based on the laws you identified:
- For the Product Law, you're adding exponents when multiplying like bases.
- For the Quotient Law, you're subtracting exponents when dividing like bases.
- For the Power Law, you're multiplying exponents when raising a power to another exponent.
- Match the Laws to their Operations
- Product of Powers matches with multiplication of like bases.
- Quotient of Powers matches with division of like bases.
- Power of a Power matches with raising one exponent to another.
- Product of Powers: Multiplication of like bases
- Quotient of Powers: Division of like bases
- Power of a Power: Raising one exponent to another
More Information
Exponent laws are fundamental in algebra and are widely used in higher mathematics. They simplify expressions and help solve equations involving powers.
Tips
- Confusing the Product and Quotient laws by mixing up addition and subtraction of exponents. Remember, use addition for multiplication and subtraction for division.
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