1. PRECALCULUS NYOS CHARTER SCHOOL QUARTER 3 “THE ESSENCE OF MATHEMATICS IS NOT TO MAKE SIMPLE THINGS COMPLICATED, BUT TO MAKE COMPLICATED THINGS SIMPLE.” ~S. GUDDER Exponents

2.  A number is written in scientific notation when it is in the form a * 10 n where 1 ≤ a < 10

3. Exponents Example: Write 152,000,000 in scientific notation.

4. Exponents Example: Write 152,000,000 in scientific notation. = 1.52 * 10 8

5. Exponents Example: Write 0.0000000068 in scientific notation.

6. Exponents Example: Write 0.0000000068 in scientific notation. = 6.8 * 10 -9

7. Exponents PropertyDefinitionExample Producta m a n = a m+n 5 3 5 7 = 5 10 Power of a Power Power of a Quotient Power of a Product Quotient

8. Exponents PropertyDefinitionExample Producta m a n = a m+n 5 3 5 7 = 5 10 Power of a Power(a m ) n = a mn (2 5 ) 4 = 2 20 Power of a Quotient Power of a Product Quotient

9. Exponents PropertyDefinitionExample Producta m a n = a m+n 5 3 5 7 = 5 10 Power of a Power(a m ) n = a mn (2 5 ) 4 = 2 20 Power of a Quotient Power of a Product Quotient

10. Exponents PropertyDefinitionExample Producta m a n = a m+n 5 3 5 7 = 5 10 Power of a Power(a m ) n = a mn (2 5 ) 4 = 2 20 Power of a Quotient Power of a Product(ab) m = a m b m (2x) 3 = 2 3 x 3 = 8x 3 Quotient

11. Exponents PropertyDefinitionExample Producta m a n = a m+n 5 3 5 7 = 5 10 Power of a Power(a m ) n = a mn (2 5 ) 4 = 2 20 Power of a Quotient Power of a Product(ab) m = a m b m (2x) 3 = 2 3 x 3 = 8x 3 Quotient

12. Exponents