Lesson 16
Equivalent Exponential Expressions
Let's investigate expressions with variables and exponents.
Problem 1
Evaluate each expression if \(x=3\).
- \(2^x\)
- \(x^2\)
- \(1^x\)
- \(x^1\)
- \(\left(\frac12\right)^x\)
Problem 2
Evaluate each expression for the given value of each variable.
-
\(2 + x^3\), \(x\) is 3
-
\(x^2\), \(x\) is \(\frac{1}{2}\)
-
\(3x^2+y\), \(x\) is 5 \(y\) is 3
-
\(10y + x^2\), \(x\) is 6 \(y\) is 4
Problem 3
Decide if the expressions have the same value. If not, determine which expression has the larger value.
-
\(2^3\) and \(3^2\)
-
\(1^{31}\) and \(31^1\)
-
\(4^2\) and \(2^4\)
- \(\left(\frac12\right)^3\) and \(\left(\frac13\right)^2\)
Problem 4
Match each equation to its solution.
Problem 5
An adult pass at the amusement park costs 1.6 times as much as a child’s pass.
-
How many dollars does an adult pass cost if a child’s pass costs:
$5?
$10?
\(w\) dollars?
- A child’s pass costs $15. How many dollars does an adult pass cost?
Problem 6
Jada reads 5 pages every 20 minutes. At this rate, how many pages can she read in 1 hour?
-
Use a double number line to find the answer.
![Double number line. Pages read. Time in minutes.](https://cms-im.s3.amazonaws.com/c1TywVBfBpwXEQG6xAu8XDop?response-content-disposition=inline%3B%20filename%3D%226-6.2.D4.PP.Image.Rev.0101.png%22%3B%20filename%2A%3DUTF-8%27%276-6.2.D4.PP.Image.Rev.0101.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T182256Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=0b21f44d218c1ae769dc91ceaa3376dec1282f2d4a456c5cc0fbe7d8ec0ee924)
- Use a table to find the answer.
pages read |
time in minutes |
---|---|
5 | 20 |
Which strategy do you think is better, and why?