![Powers of -1 Write out (-2) 3 (-2)*(-2)*(-2) When the exponent is an odd number, the answer can be negative. [(-2)*(-2)]*(-2)= [+4] * (-2) = -8](https://image.slidesharecdn.com/82powerofpower-1221711181533635-9/85/8-2power-Of-Power-16-320.jpg)
8 2power Of Power
- 1. Power of a Power Finding powers of numbers with exponents (x m ) n = x mn
- 2. Simplify (2 3 ) 2 This means 2 3 *2 3 2 3 *2 3 = (2*2*2)*(2*2*2)=2 6
- 3. Simplify (4 2 ) 3 This means 4 2 *4 2 *4 2 4 2 *4 2 *4 2 = (4*4)*(4*4)*(4*4)=4 6
- 4. How does this work? Look again (4 2 ) 3 = 4 6 (2 3 ) 2 =2 6 How do the exponents 2 and 3 relate to the exponent 6?
- 5. Let’s look at some more (3 3)4 = (3*3*3)*(3*3*3)*(3*3*3)*(3*3*3) (3 3)4 =3 ?? 3x4 = 12 As you can see (3 3)4 shows 3 multiplied by itself 12 times. (3 3)4 = 3 3*4 =3 12
- 6. Let’s try some using the Power of Powers Property The Power of Powers Property states that when you have a number to a certain power raised to another power, you multiply the exponents. Examples (3 3)4 = 3 12 (8 2)5 = 8 10 (9 1)4 = 9 4
- 7. Try some (2 3)4 = ? (10 3)2 = ? (p 2)5 = ? (x m)3 = ? Go to the next slide when you have the solutions to check your work.
- 8. Power of Powers (2 3)4 = 2 12 (10 3)2 = 10 6 (p 2)5 = p 10 (x m)3 = x 3m
- 9. Lesson 8.2 Part Two
- 10. Raise a monomial to a power (xy) 2 = xy*xy = x*x*y*y = x 2 y 2 (xy 2 ) 2= If you get stuck with powers of powers, try writing out the multiplication of numbers and variables. (x*y*y)* (x*y*y) = x*y*y*x*y*y = x*x*y*y*y*y = x 2 y 4
- 11. Try some (xy )2 = ? (xy 2)2 = ? (πr 2)4 = ? Go to the next slide when you have the solutions to check your work.
- 12. Solutions (x 1 y )2 = x 2 y 2 (x 1 y 2)2 = x 2 y 4 (π 1 r 2)4 = π 4 r 8 Can you see the power of powers property at work? If not, try changing the variables that have no exponent to an exponent of one. {Once again, 1 comes in handy!}
- 13. Let’s take another look (x 1 y )2 = x 2 y 2 (x 1 y 2)2 = x 2 y 4 (π 1 r 2)4 = π 4 r 8
- 14. Try some more. Use 1 to your advantage when you can. (x 2 y) 3 = (x 2 y1) 3 = x 2*3 *y 1 * 3 = x 6 y 3 (x 2 y 2 z 2 ) 3 = (abcd) n = (x 2 y 3 ) 5 =
- 15. Solutions (x 2 y 2 z 2 ) 3 =x 2*3 y 2*3 z 2*3 =x 6 y 6 z 6 (abcd) n =a n b n c n d n (x 2 y 3 ) 5 =x 2*5 y 3*5 = x 10 y 15
- 16. Powers of -1 Write out (-2) 3 (-2)*(-2)*(-2) When the exponent is an odd number, the answer can be negative. [(-2)*(-2)]*(-2)= [+4] * (-2) = -8
- 17. Suggestion Once again, the suggestion is to write out the multiplication statements to help you solve tricky exponential products.
- 18. Simplify (-t) 5 =? (-t) 4 =? (-5x) 3 =?
- 19. solutions (-t) 5 = (-t) * (-t) * (-t) * (-t) * (-t) =-t 5 (-t) 4 =t 4 (-5x) 3 =(-5x) (-5x) (-5x) = = -5*-5*-5*x*x*x = -125x 3