Transcript 8.2 Laws of Exponents: Powers and Products

Page 377 – Laws of Exponents:
Powers and Products
Objectives
Find the power of a power.
Find the power of a product.
8.2 Laws of Exponents: Powers and Products
Glossary Terms
Power-of-a-Power Property
Power-of-a-Product Property
Rules and Properties
Power-of-a-Power Property
For all nonzero real numbers x and all
integers m and n, (xm)n = xmn.
When you have a power raised to a
power, multiply the exponents.
Simplify and find the value of each
expression if possible.
(2³)4 = 23·4 = 212 = 4096
(10³)² = 103·2 = 106 = 1,000,000
(p2)5 = P2·5 = p10
(xm)2 = xm·2 = x2m
Rules and Properties
Power-of-a-Product-Property
For all real numbers, x and y, and all
integers n,
(xy)n = xnyn
The exponent goes with everything inside the
parentheses.
It can be extended to include any number of factors
inside the parentheses.
Simplify
(x²y)³ = x2·3 · y1·3 = x6y3
(ab²cn)5 = a1·5 · b2·5 · cn·5 = a6b10c5n
8.2 Laws of Exponents: Powers and Products
Rules and Properties
Powers of –1
Even powers of –1 are equal to 1.
Odd powers of –1 are equal to –1.
Simplify
(-t)5 = (-1·t)5 = (-1)5 · t5 = -1 · t5 = -t5
-t4 = This is already in simplest form. The
exponent applies only to t.
(-5x)³ = (-5)³ · x³ = -125x³
8.2 Laws of Exponents: Powers and Products
Key Skills
Use the properties of exponents to
simplify an expression.
Simplify n3(2k2n4)2
Use the Power-of-aProduct Property.
Use the Power-of-aPower Property.
Use the Product-ofPowers Property.
TOC
= n3  22  (k2)2(n4)2
=
n3

4

.2
2
k

.2
4
n
= n3  4  k4  n8
= 4  k4  n3+8
= 4k4n11
Assignment
Page 381
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#26 –52 even, 54 – 63