What is the simplified form of 41/2 ? (1 point) 41/2 = Question 2 What rational number could be used as an exponent to rewrite 20−−√^5 ?(1 point) The rational number that could be used as an exponent is

Answer 1

To simplify the expression \( \frac{41}{2} \):

1. The fraction \( \frac{41}{2} \) can be divided into a whole number and a fraction.
2. Dividing 41 by 2 gives us 20 with a remainder of 1, so: \[ \frac{41}{2} = 20 \frac{1}{2} = 20.5 \] Thus, the simplified form of \( \frac{41}{2} \) is \( 20.5 \).

Answer to question 1: \( 20.5 \)

For question 2, we want to rewrite \( \sqrt{20}^5 \) using a rational number as an exponent.

1. We can express the square root using exponents: \[ \sqrt{20} = 20^{1/2} \]
2. Thus, raising \( \sqrt{20} \) to the 5th power gives: \[ \sqrt{20}^5 = (20^{1/2})^5 \]
3. According to the laws of exponents, when raising a power to a power, we multiply the exponents: \[ (20^{1/2})^5 = 20^{(1/2) \cdot 5} = 20^{5/2} \]

Therefore, the rational number that could be used as an exponent to rewrite \( \sqrt{20}^5 \) is \( \frac{5}{2} \).

Answer to question 2: \( \frac{5}{2} \)