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5.2 Integer Exponents and The Quotient Rule

5.2 Integer Exponents and The Quotient Rule. 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. .

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5.2 Integer Exponents and The Quotient Rule

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  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:

  8. 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:

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

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

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

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