Co n cep t Byt e
Use W ith Lesson 7-3Po w er s of Po w er s
and Powers of Product s
Co m m o n Co r e St at e St a n d a r d s
Pr ep ar es f o r N-RN.A.1 Explain ho w the
d e fin itio n o f th e meaning o f rational exponents
fo llo w s fro m extending the properties o f integer
exponents to those values...
MP 7 ~You can use patterns to find a shortcut for simplifying a power raised to a power or a
product raised to a power.Activity 1
Copy and complete each statement in Exercises 1-9.- (45) 2 = 4 5 • 4 5 = 4 ®+ = 45 i = 4
- (36)3 = 36 • 36 • 36 = 3h +b+* = 36'
- (58)4 = 58 • 58 • 51
= 3®
58 = 5 «+B+B+»: 58’" = 5s- (4s)3 = 43 • 43 • 43 = 4 + + =^45 =^4
5. ( 52 ) = 52 • 52 • 52 • 52 = 5: : S H = 5 - (a4) 2 = a 4
- (n2) 3 = = « + +
- (x5) 4 =
9. (a<)4
aB+B.aA.m =^ a
n *^2 * a; = n^
XB +B+B +B = ^5-B = xi
a®+B+B+B = fl|-B _ am- a. Look f o r a Pat t ern What pattern do you see in your answers to Exercises 1-9?
b. Predict Use your pattern to simplify (y11)33.
Activity 2
Copy and complete each statement in Exercises 11-15.- (3ri)2 = 3n • 3n = (3 • 3) (n • n) = 3 n
- ( 2 x)3 = 2 x • 2 x • 2x = (2 • 2 • 2 ) (x • x • x) = 2 'x*
- {ab)2 = ab • ab = {a • a){b • b) = a*bm
- (xy)3 = xy • xy • xy = ( • • )( • • ) =x"y"
- =
- a. Look f o r a Pat t ern What pattern do you see in your answers to
Exercises 11-15?
b. Predict Use your pattern to simplify (rs)20.
432 Concept Byte Po w er s o f Po w er s an d Po w er s o f Pro d uct s