Evaluate Exponential Expressions: Mini-Lesson Review

Mini Lesson Question

Question #3: Evaluate Exponential Expressions

Evaluate

2(4)^3

Evaluating Exponential Expressions

A power is repeated multiplication of the same factor. The factor is the base, and the number of times the base is used as a factor is the exponent. The expression is called a power.

$B a s e \to {\underset{⏟}{5^{3}}}^{\leftarrow E x p o n e n t}$

The expression $5^{3}$ is read:

five to the power of three
five to the third power
five cubed

$5^{3}$ means 5 is used as a factor 3 times: $5^{3} = 5 \cdot 5 \cdot 5 = 125$ .

Evaluate each expression.

$(\frac{1}{2})^{5}$

Use $\frac{1}{2}$ as a factor 5 times.

$(\frac{1}{2})^{5} = \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} = \frac{1}{32}$

$(\frac{1}{2})^{5} = \frac{1}{32}$
$7 (3)^{4}$

Use order of operations. Evaluate the exponent first.

$7 (3)^{4} = 7 (3 \cdot 3 \cdot 3 \cdot 3) = 7 (81)$

Then multiply.

$7 (81) = 567$

$7 (3)^{4} = 567$
$20 (0.8)^{2}$

Use order of operations. Evaluate the exponent first.

$20 (0.8)^{2} = 20 (0.8 \cdot 0.8) = 20 (0.64)$

Then multiply.

$20 (0.64) = 12.8$

$20 (0.8)^{2} = 12.8$

Try it

Try It: Evaluating Exponential Expressions

Evaluate $50 (0.2)^{2}$ .

Here is how to evaluate this exponential expression.

Step 1 - Use order of operations and evaluate the power first.

$50 (0.2)^{2} = 50 (0.2 \cdot 0.2) = 50 (0.04)$

Step 2 - Next, multiply. $50 (0.04) = 2$

$50 (0.2)^{2} = 2$

Check Your Understanding

Evaluate $2 (3)^{3}$ .

The answer is 54.

Check yourself: Use order of operations and evaluate the power first. Then multiply the result by 2.