1. MULTIPYING POWERS LESSON 15

2. 42424242 BASE EXPONENT POWER

3. EXPONENT LAW 1 PRODUCT OF POWERS PRODUCT OF POWERS n a x n b = n a+b n a x n b = n a+b Multiplying powers with the same base Multiplying powers with the same base

4. n a x n b = n a+b (Product of Powers) same base:To multiply powers with the same base: KEEP THE BASE KEEP THE BASE ADD THE EXPONENTS ADD THE EXPONENTS EXAMPLE: EXAMPLE: 3 3 x 3 4 = 3 7 3 3 x 3 4 = 3 7

5. WHY: 3 3 = (3x3x3) 3 4 = (3x3x3x3) Therefore: 3 3 x 3 4 3 3 x 3 4 = (3x3x3)(3x3x3x3) 3 7 = 3 7 Meaning of the power

6. EXAMPLE 4 4 x 4 9 4 4 x 4 9 Write as a single Power Write the meaning Give the value

7. EXAMPLE: 4 4 x 4 9 4 4 x 4 9 Write as a single PowerWrite as a single Power 4 4 x 4 9 = 4 13 4 4 x 4 9 = 4 13 Write the meaningWrite the meaning (4x4x4x4)(4x4x4x4x4x4x4x4x4) =(4x4x4x4x4x4x4x4x4x4x4x4x4) Give the valueGive the value 4 13 = 67108864

8. EXAMPE 2: 5= -4 5 () x -4 5 () 2 -4 5 () 3 (1.1) 3 (1.1) 2 (1.1) = (1.1) 6 Exponent of 1 you don’t have to show it

9. EXAMPLE 3 (4 3 x 4 5 ) 3 = (4 3 x 4 5 )(4 3 x 4 5 )(4 3 x 4 5 ) = (4 8 )(4 8 )(4 8 ) = (4 8+8+8 )=(4 24 ) SINGLE POWER MEANING

10. EXPONENT LAW 2 POWER OF A POWER (x m ) n = x mn (x m ) n = x mn Multiply the two powers together. Multiply the two powers together. Example: Example: (5 2 ) 3 = 5 6 (5 2 ) 3 = 5 6

11. (x m ) n = x mn EXAMPLE – (x m ) n = x mn (3 2 x 3 4 ) 3 = (3 6 ) 3 = (3 6 )(3 6 )(3 6 ) = (3 18 )

12. EXAMPLE 2 – Find the value NOT THE SAME BASE FIND VALUE FOR EACH POWER FOLLOW ORDER OF OPERATIONS (43 x 52)3 =(64 x 25)3 =(1600)3 = 4 096 000 000