Question

Match the expression to the method needed to evaluate.

1. Add the exponents.
2. Multiply the exponents.
3. Write as a product of powers.
4. Subtract the exponents.

Expressions:
1. 4^3 * 4^5
2. (5^3)^3
3. 5^3 / 5^2
4. 4^3 * 4^2

A) 1 - Add the exponents, 2 - Multiply the exponents, 3 - Write as a product of powers, 4 - Subtract the exponents
B) 1 - Multiply the exponents, 2 - Add the exponents, 3 - Subtract the exponents, 4 - Write as a product of powers
C) 1 - Subtract the exponents, 2 - Multiply the exponents, 3 - Write as a product of powers, 4 - Add the exponents
D) 1 - Add the exponents, 2 - Multiply the exponents, 3 - Subtract the exponents, 4 - Write as a product of powers

Answer 1

To evaluate exponential expressions, we use specific arithmetic rules on the exponents. For multiplication of the same bases, we add the exponents; for raising an exponent to another, we multiply the exponents; and for division of the same bases, we subtract the exponents. The correct answer is D: 1 - Add the exponents, 2 - Multiply the exponents, 3 - Subtract the exponents, 4 - Add the exponents.

Step-by-step explanation:

To match the expressions with the correct method of evaluation for exponents, we can apply known rules for dealing with exponential expressions. Here's how we evaluate each expression:

1. 4^3 * 4^5 - When multiplying exponents with the same base, you add the exponents. So, this expression corresponds to Add the exponents.
2. (5^3)^3 - When you raise an exponent to another exponent, you multiply the exponents. This expression corresponds to Multiply the exponents.
3. 5^3 / 5^2 - When dividing exponents with the same base, you subtract the exponents. This expression corresponds to Subtract the exponents.
4. 4^3 * 4^2 - This is another example of multiplication of exponents with the same base, and again you add the exponents. This expression also corresponds to Add the exponents.

The correct match would therefore be:

• Expression 1 (4^3 * 4^5) - Add the exponents
• Expression 2 ((5^3)^3) - Multiply the exponents
• Expression 3 (5^3 / 5^2) - Subtract the exponents
• Expression 4 (4^3 * 4^2) - Add the exponents

The answer is D:

1. Add the exponents
2. Multiply the exponents
3. Subtract the exponents
4. Add the exponents