7-1 Zer o an d N eg at i v e Ex p o n en t scpor
Quick Review
You can use zero an d negative integers as exponents.
For every nonzero n u m b e r a, a0 = 1. For every nonzero
number a an d any integer n, a~n = jy,. W hen you evaluate
an exponential expression, you can simplify the expression
before substituting values for th e variables.Example
What is the value of a2b~4c° for a = 3, b = 2, and
c= -5?a2b 4 c° = b4
A 1)
h4- 24
9
16
Use the d e fin itio n o f negative exponents.Use th e d e fin itio n o f zero exponent.Substitute.Simplify.Exercises
Simplify each expression.- 5°
8 .4x
-2
y,—8- 7“ 2
p2q 4r°
Evaluate each expression for x = 2, y- x°y2
- x°z° 13. %
y
— 3, and z = — 5.- ( - x ) - y
v-0 - y-2,2 15. 2x
y2z~l - Reasoning Is it true th at ( - 3b)4 = -1 2 b 4? Explain
why or why not.
7-2 Multiplying Powers Wit h the Same Base
Quick Review Exercises \
To multiply pow ers with th e sam e base, ad d the exponents. Complete each equation. j
am • an = am+n, w here a + 0 and m and n are 17. 32 • 3 = 310 18. a6 • am = a8
real n um bers
... 11 Ifn „,I| 1 ||I |«, ||---- Ittrn--...-------------r-ir*Tvnvra..in.iTirironmmiitiimiiffliji n-iTmrxar i r-r-r >•- -----__,.................... - -A 19. x 2v5 • x y = x 5y41^20. ah • a = a
Example
HSI S' II
rsiT— * 22. mw • m n = mmWhat is the simplified form of each expression? Simplify each expression.
a. 310 • 34 = 310+4 = 314 23. 2d2^ • d^3 24. (x3)(x4)b. («4)(a3) = a4+3 = a‘
- (x3y5)(-y 7x) 26. (si)(sl)
c. (xi)(xs) =X^+5 = X 5- {psq){qip) 28. 2mm2 • 3mm
d.(b«)(b^) = b?+5 = b4+4 = b?- Estimation Each square in ch of your body has about
6.5 X 102 pores. Suppose th e back of your h a n d has
a n area of ab o u t 0.12 X 102 in.2. About how m any
p ores are on the back of your hand? W rite your
answer in scientific notation.
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