# Lesson 15

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 6, 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.