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.