Which of the following expressions is equivalent to 16^1/4/√49

Question

? Use the properties of exponents to help determine the answer.(1 point)
Responses

2/7
Start Fraction 2 over 7 End Fraction

1/2
Start Fraction 1 over 2 End Fraction

2
2

4/7
Start Fraction 4 over 7 End Fraction

Answer 1

To simplify the expression \( \frac{16^{1/4}}{\sqrt{49}} \), we can follow these steps:

1. Simplify \( 16^{1/4} \): \[ 16 = 2^4 \] Thus, \[ 16^{1/4} = (2^4)^{1/4} = 2^{4 \cdot (1/4)} = 2^1 = 2 \]

2. Simplify \( \sqrt{49} \): \[ \sqrt{49} = 7 \]

3. Combine the results: Now substitute these values back into the expression: \[ \frac{16^{1/4}}{\sqrt{49}} = \frac{2}{7} \]

Therefore, the answer is: \[ \frac{2}{7} \]

The correct response is: Start Fraction 2 over 7 End Fraction.