Certainly! Let’s analyze and match each given expression to the appropriate method needed to evaluate it by recognizing the rules of exponents that apply.
1. Expression: [tex]\((4x^3)^5\)[/tex]
Rule: When you have a power of a power, you multiply the exponents.
Method: Multiply the exponents
2. Expression: [tex]\(5^3 \cdot 5^3\)[/tex]
Rule: When you multiply like bases, you add the exponents.
Method: Add the exponents
3. Expression: [tex]\((7^2)^3\)[/tex]
Rule: When you have a power of a power, you multiply the exponents.
Method: Multiply the exponents
4. Expression: [tex]\(6^9 \div 6^5\)[/tex]
Rule: When you divide like bases, you subtract the exponents.
Method: Subtract the exponents
To summarize:
1. [tex]\((4x^3)^5\)[/tex]: Multiply the exponents
2. [tex]\(5^3 \cdot 5^3\)[/tex]: Add the exponents
3. [tex]\((7^2)^3\)[/tex]: Multiply the exponents
4. [tex]\(6^9 \div 6^5\)[/tex]: Subtract the exponents
These methods are fundamental rules of exponents which help simplify and evaluate expressions involving powers.
