Objectives Evaluate expressions containing zero and integer exponents. Simplify expressions containing zero and integer exponents.

When the exponent decreases by one, the value of the power is divided by 5. Continue the pattern of dividing by 5.

Example 1: Application One cup is 2–4 gallons. Simplify this expression. gal is equal to

Example 2: Zero and Negative Exponents Simplify. A. 4–3 B. 70 Any nonzero number raised to the zero power is 1. 7º = 1 C. (–5)–4 D. –5–4

Check It Out! Example 3b Evaluate the expression for the given values of the variables. for a = –2 and b = 6 Substitute –2 for a and 6 for b. Evaluate expressions with exponents. Write the power in the denominator as a product. Evaluate the powers in the product. 2 Simplify.

What if you have an expression with a negative exponent in a denominator, such as ? Definition of a negative exponent. Substitute –8 for n. Simplify the exponent on the right side. An expression that contains negative or zero exponents is not considered to be simplified. Expressions should be rewritten with only positive exponents. So if a base with a negative exponent is in a denominator, it is equivalent to the same base with the opposite (positive) exponent in the numerator.