Chapter A.1, Problem 82E

Solution

Replace | | with <, = , or > to make a true statement.

  $4^{-2/3}<3^{-3/4}$ .

Given:

The given statement is $4^{-2/3}$ $\left|\right|$ $3^{-3/4}$ .

Concept Used:

• The greater than symbol means the number on the left is greater than the number on the right.
• The greater than or equal symbol means the number on the left is greater than or equal to the number on the right.
• The less than symbol means that the number on the left is less than the number on the right.

Calculation:

The given statement is $4^{-2/3}$ $\left|\right|$ $3^{-3/4}$ .

  $4^{-2/3}=0.40$

  $3^{-3/4}=0.44$

  $0.40<0.44$

Therefore $4^{-2/3}<3^{-3/4}$ .

Thus $4^{-2/3}$ is less than $3^{-3/4}$ .