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.
 Use a table to find the answer.
pages read 
time in minutes 

5  20 
Which strategy do you think is better, and why?