Base x Exponent Remember! 4

2–4 is read “2 to the negative fourth power.” Reading Math

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

Example 2 A sand fly may have a wingspan up to 5–3 m. Simplify this expression. 5-3 m is equal to

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

In (–3)–4, the base is negative because the negative sign is inside the parentheses. In –3–4 the base (3) is positive. Caution

Example 4 Simplify. a. 10–4 b. (–2)–4 c. (–2)–5 d. –2–5

Example 7 Evaluate the expression for the given value of the variable. p–3 for p = 4 Substitute 4 for p. Evaluate exponent. Write the power in the denominator as a product. Evaluate the powers in the product.

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.

Quiz 1. A square foot is 3–2 square yards. Simplify this expression. Simplify. 2. 2–6 3. (–7)–3 4. 60 1 5. for a = 6 and b = 3

Lesson Quiz: Part II Evaluate each expression for the given value(s) of the variables(s). 6. x–4 for x =10 7. for a = 6 and b = 3