5.2 Integer Exponents and The Quotient Rule

1. 5.2Integer Exponents and The Quotient Rule

2. For Example: Each time the exponent is reduced by 1, the value is divided by 2 (the bases). Using this pattern, the list can be continued to smaller and smaller integers. From the preceding list, it appears that we should define 20 as 1 and negative exponents as reciprocals. For any nonzero real number a, a0= 1. Example: 170= 1

3. EXAMPLE 1 • Evaluate. Solution:

4. For any nonzero real number a and any integer n, Since and , we can deduce that 2−n should equal

5. EXAMPLE 2 • Simplify. Solution:

6. Consider the following: Therefore, For any nonzero numbers aand b and any integers mand n, and Example: and

7. EXAMPLE 3 • Simplify by writing with positive exponents. Assume that all variables represent nonzero real numbers. Solution:

9. Use the quotient rule for exponents. We know that Notice that the difference between the exponents, 5− 3 = 2, this is the exponent in the quotient. This example suggests the quotient rule for exponents. For any nonzero real number aand any integer mand n, (Keep the same base; subtract the exponents.) Example:

10. Simplify by writing with positive exponents. Assume that all variables represent nonzero real numbers. Solution:

12. Solution: • Simplify. Assume that all variables represent nonzero real numbers.

13. Homework • 5.1: 1 – 87 EOO • 5.2: 1 – 77 ODD