Evaluate Exponential Expressions: Mini-Lesson Review

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.

$Base\to {\underbrace{5^3}}^{\leftarrow Exponent}$

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: $5^3=5·5·5=125$.

Evaluate each expression.

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

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

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

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

2. $7(3{)}^4$

   Use order of operations. Evaluate the exponent first.

   $7(3{)}^4=7(3·3·3·3)=7(81)$

   Then multiply.

   $7(81)=567$

   $7(3{)}^4=567$

3. $20(0.8{)}^2$

   Use order of operations. Evaluate the exponent first.

   $20(0.8{)}^2=20(0.8·0.8)=20(0.64)$

   Then multiply.

   $20(0.64)=12.8$

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