Transcript Chapter 8.1 Notes: Apply Exponent Properties Involving

Chapter 8.1 Notes: Apply
Exponent Properties Involving
Products
Goal: You will use properties of exponents
involving products.
• Important terms:
– base
– power
– exponent
• Product of Powers Property:
To multiply powers having the same base, add the
exponents.
i.e. am • an = am + n
i.e. 56 • 53 = 56 + 3 = 59
i.e. 3x3y5 • -2x8y • -4x2y3
Ex.1: Simplify the expression.
a. (-2)3 • (-2)5
b. x4 • x3
c. 76 • 7 • 78
d. -2x3y • x6y3 • 5xy2
Ex.2: Simplify the expression.
a. 32 • 37
b. (-5) • (-5)9
c. -6y3z5 • -9y9z5
d. x2 • x6 • x
Ex.3: Which expression is equivalent to w3w2?
A. w3w3
B. w4w
C. w5w
D. w9w4
• Power of a Power Property:
To find a power of a power, multiply the exponents.
i.e. (am)n = amn
i.e. (34)2 = 3 4 • 2 = 38
i.e. (2x3y5z3)3
Ex.4: Simplify the expression.
a. (25)3
b. [(-6)2]5
c. (2x2y6)4
d. [(y + 2)6]2
Ex.5: Simplify the expression.
a. m8 • m9
b. (42)2
c. [(-2)4]5
d. (-3x5y8z3)3
• Power of a Product Property:
To find a power of a product, find the power of each
factor and multiply.
i.e. (ab)m = ambm
i.e. (2x4y3)3 = 23x 4•3 y 3•3 = 8x12y9
Ex.6: Simplify each expression.
a. (4mn)3
b. (9xy)2
c. (-4z)2
d. – (4z)2
Ex.7: Simplify (2x3)2 • x4
Ex.8: Simplify the expression.
a. (-3n2p3)2 • (2n3p4)3
b. (9m3n)4
c. 5 • (5x2)4
d. (2xy3z4)2 • (4x3y5z)3