Lesson 16

Equivalent Exponential Expressions

Let's investigate expressions with variables and exponents.

Problem 1

Evaluate each expression if \(x=3\).

  1. \(2^x\)
  2. \(x^2\)
  3. \(1^x\)
  4. \(x^1\)
  5. \(\left(\frac12\right)^x\)

Problem 2

Evaluate each expression for the given value of each variable.

  1. \(2 + x^3\), \(x\) is 3 

  2. \(x^2\), \(x\) is \(\frac{1}{2}\) 

  3. \(3x^2+y\), \(x\) is 5 \(y\) is 3 

  4. \(10y + x^2\), \(x\) is 6 \(y\) is 4

Problem 3

Decide if the expressions have the same value. If not, determine which expression has the larger value.

  1. \(2^3\) and \(3^2\)

  2. \(1^{31}\) and \(31^1\)

  3. \(4^2\) and \(2^4\)

  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.

  1. How many dollars does an adult pass cost if a child’s pass costs:

    $5?

    $10?

    \(w\) dollars?

  2. A child’s pass costs $15. How many dollars does an adult pass cost?
(From Unit 4, Lesson 6.)

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.
  • Use a table to find the answer.
pages
read
time in
minutes
5 20

Which strategy do you think is better, and why?

(From Unit 2, Lesson 10.)