1. Exponent Laws Part I Topic 2.4

2. Exponent Law for a Product of Powers How could you solve this question? What do you notice about the bases? Will it work if the bases are not the same? What does product mean? What happens to the exponents?

3. Law 1 To multiply powers with the same base, simply leave the base the same and add the exponents. n a x n b = n a+b

4. The “Law” To multiply powers with the same base, simply leave the base the same and add the exponents. EXAMPLES

5. 6 5 x 6 4 = = (6 x 6 x 6 x 6 x 6) x (6 x 6 x 6 x 6) = 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6 = 6 9 = 6 5+4 = 10077696 Why does this work? 6565 6464

6. What do you think happens here? The rule does NOT apply to ADDITION of same base questions. The rule does NOT apply to UNLIKE base multiplication questions. Follow BEDMAS!

7. Exponent Law for a Quotient of Powers How could you solve this question? What does quotient mean? What do you notice about the bases? Will it work if the bases are not the same? What happens to the exponents?

8. Law 2 To divide powers with the same base simply leave the base the same and subtract the exponents. n a ÷ n b = n a-b

9. The “Law” To DIVIDE powers with the SAME base, SUBTRACT the exponents. EXAMPLES You might find it easier to write division questions in ‘fraction form’!

10. Why does this work?

11. What do you think happens here? Law does NOT apply to SUBTRACTION of same base questions. Law does NOT apply to UNLIKE base DIVISION questions. Follow BEDMAS!

12. Let’s try a few… Write as a power. Evaluate.

14. ASSIGNMENT PAGE 76 Discuss: #1, 2, 3 Complete: 4aceg, 5bdfh, 6, 8, 9, 10aceghij, 12abd, 13aceg, 17 Extension: 20, 21a, 22a