Matching the Rules of Exponents

Match each expression to the method needed to evaluate it.

Expressions:
1. [tex]\(\left(4 x^3\right)^5\)[/tex]
2. [tex]\(5^3 \cdot 5^3\)[/tex]
3. [tex]\(\left(7^2\right)^3\)[/tex]
4. [tex]\(6^9 \div 6^5\)[/tex]

Methods:
A. Write as a product of powers.
B. Subtract the exponents.
C. Add the exponents.
D. Multiply the exponents.



Answer :

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.