Which of the expressions shown evaluate to positive rational numbers? Select all that apply.

Question

A. (-1.01) to the power of 4
B. (-5/6) to the power of 2
C. (-1/2) to the power of 3
D. (2.75) to the power of 2 - 3 to the power of 2
E. 3 to the power of 4 - 10 to the power of 2

Answer 1

Let’s evaluate each expression to determine which ones yield positive rational numbers.

A. \((-1.01)^4\)
Any negative number raised to an even power results in a positive number. Therefore, \((-1.01)^4 = 1.01^4\), which is a positive rational number.

B. \((-5/6)^2\)
Similarly, a negative number raised to an even power results in a positive number. Thus, \((-5/6)^2 = (5/6)^2\), which is also a positive rational number.

C. \((-1/2)^3\)
A negative number raised to an odd power results in a negative number. Thus, \((-1/2)^3 = -1/8\), which is a negative number and not a positive rational number.

D. \(2.75^2 - 3^2\)
Calculating each part:
\(2.75^2 = 7.5625\)
\(3^2 = 9\)
So, \(2.75^2 - 3^2 = 7.5625 - 9 = -1.4375\), which is negative and not a positive rational number.

E. \(3^4 - 10^2\)
Calculating each part:
\(3^4 = 81\)
\(10^2 = 100\)
So, \(3^4 - 10^2 = 81 - 100 = -19\), which is negative and not a positive rational number.

Therefore, the expressions that evaluate to positive rational numbers are:

A and B.