Question

Simplify the expression 3^(1/4) • 3^2 to show the product of powers property. Show any intermittent steps that demonstrate how you arrived at the simplified answer.

Options:
A) 3^(9/4)
B) 3^(7/4)
C) 3^(3/4)
D) 3^(5/4)

Answer 1

To simplify 3^(1/4) • 3^2, apply the product of powers property by adding the exponents. The expression simplifies to 3^(9/4), which is option A.

Step-by-step explanation:

The question asks to simplify the expression 3^(1/4) • 3^2 using the product of powers property. The product of powers property states that when you are multiplying two exponents with the same base, you can add the exponents. Here's the step-by-step breakdown of the simplification:

1. Write down the expression: 3^(1/4) • 3^2
2. Apply the product of powers property: 3^((1/4) + 2)
3. Convert the whole number exponent to a fraction: 3^((1/4) + (8/4))
4. Add the exponents: 3^((1/4) + (8/4)) = 3^(9/4)
5. Thus, the simplified expression is: 3^(9/4)

The correct answer is option A) 3^(9/4).