Question

Elect the expression that is equal to (7(³ᵏ)³)

a. 7(³ᵏ)
b. 7(³ᵏ⁺¹)
c. 7(³ᵏ)⁺¹
d. 7(³ᵏ⁺³)

Answer 1

The expression (7(³ᵏ)³) is equal to 7(³ᵏ⁺³).

The correct answer is (d)

Step-by-step explanation:

To simplify the expression (7(³ᵏ)³), we need to apply the exponent rules. Here's how:

1. Start by simplifying the expression inside the parentheses: 7(³ᵏ).

• - This means raising 7 to the power of ³ᵏ.
• - The base 7 remains the same, and we multiply the exponents: 7³ᵏ.

2. Now, we have (7³ᵏ)³.

• - To simplify, we need to multiply the exponents.
• - Multiply 3 and ³ᵏ: (3)(³ᵏ) = ³(3ᵏ).

3. The expression simplifies to 7³(3ᵏ).

• - This means raising 7 to the power of ³, and raising 3ᵏ to the power of 1.
• - 7³ equals 7 * 7 * 7 = 343.
• - (3ᵏ)¹ is simply 3ᵏ.

4. Putting it all together, we get 343 * 3ᵏ = 7(³ᵏ⁺³).

Therefore, the expression (7(³ᵏ)³) is equal to 7(³ᵏ⁺³), making option (d) the correct answer.