Which could have been the expression Iris evaluated? Check all that apply.
[tex]$2^{-6}$[/tex]
[tex]$6^{-4}$[/tex]
[tex]$4^{-3}$[/tex]
[tex]$\left(\frac{1}{2}\right)^{-5}$[/tex]
[tex]$\left(\frac{1}{4}\right)^{-3}$[/tex]
Answer (1)
Evaluate each expression with negative exponents.
2 − 6 = 0.015625
6 − 4 ≈ 0.0007716
4 − 3 = 0.015625
( 2 1 ) − 5 = 32
( 4 1 ) − 3 = 64
All expressions could have been evaluated by Iris. Therefore, the expressions are: 2 − 6 , 6 − 4 , 4 − 3 , ( 2 1 ) − 5 , ( 4 1 ) − 3 .
Explanation
Understanding the Problem We are given a list of expressions with negative exponents, and we need to determine which of these expressions Iris could have evaluated. Since we don't know the value Iris obtained, we will evaluate each expression and consider all of them as possible answers.
Evaluating the Expressions Let's evaluate each expression:
2 − 6 = 2 6 1 = 64 1 = 0.015625
6 − 4 = 6 4 1 = 1296 1 ≈ 0.0007716
4 − 3 = 4 3 1 = 64 1 = 0.015625
( 2 1 ) − 5 = 2 5 = 32
( 4 1 ) − 3 = 4 3 = 64
Possible Answers Since we don't know the value Iris obtained, any of these expressions could have been the one she evaluated. Therefore, all the given expressions are possible answers.
Examples
Understanding exponents, especially negative exponents, is crucial in many fields. For instance, in computer science, memory sizes are often expressed in powers of 2 (e.g., kilobytes, megabytes, gigabytes). Similarly, in finance, understanding exponential decay (which involves negative exponents) is essential for calculating depreciation or the present value of future cash flows. These concepts help in making informed decisions in technology and investment scenarios.
