7-3 M ore Mult iplicat ion Propert ies of Exponent s
Quick Review
To raise a pow er to a power, m ultiply the exponents.
(am)n = a mn, w here a + 0 and m and n are real
numbers
To raise a p ro d u ct to a power, raise each factor in the
p roduct to the power.
{ab)n = anbn, w here a ¥= 0, b # 0, and n are real
numbersExercises
Complete each equation.- (55) = 515 31. (b~4) = b20
- (4x3y 5) = 16x6y 10 33. (xi) = x 2
- (a%) = a ' 35. (2x2y 4) = 4x4y 2
Simplify each expression. - (<73 r ) 4 37. (1.342)5(1.34)-8
Example
What is the simplified form of each expression?
a. (x5)7 = x 5‘7 = x 35 b. (pg)8 = psqsc. (xs)3 = X3*3 = X3 = x d. iKa b ) ^ = cblfi- (12x2y-2 )5(4xy~3)-7 39. ( —2 r_4)2( —3 r2z8)-1
- (x^)7 41.
J7-4 Division Propert ies of Exponent s
Quick Review
To divide powers w ith th e sam e base, subtract the
exponents.
am_ _ _ am nt w here a =£ 0 and m and n are integersTo raise a q uotient to a power, raise th e n u m era to r a n d the
d enom inator to th e power.
( f ) ” = f " ’ w^ ere « ^ 0, h # 0, an d n is an integer
V..... *4Exercises
Simplify each expression.
- w5 3 x 1
«• (f 4, (*?)-
- w5 3 x 1
Simplify each quotient. Write your answer in
scientific notation.Example
What is the simplified form of | j?( 5x4 (5*4)3 53x4' 3 125 x 12
I z2 J (z2)3 ~ z2'3 z6- 4-2 x 10 4 7. 31 X lp4„
2.1 X 1011 1.24 X 102
48.4-5X1? 9 X 107 49.51X1°!1.7 X 102 - W riting List th e steps th a t you w ould use to
simplify ( ) 3.
476 Ch ap t er 7 Ch ap t er Revi ew