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# Algebra 6 Point 2

## by herbison on Feb 26, 2010

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## Algebra 6 Point 2Presentation Transcript

• 6.2 Powers of Monomials
Objective:
• To simplify a power of a power and a power of a product
Frameworks: 10.P.1, 10.P.7
• What is 334?
334= (3*3*3)*(3*3*3)*(3 *3* 3)*(3*3*3)
= 312
What is the pattern?
• Multiplying Monomials
To raise a power to a power, you multiply the exponents and keep the same base.
• Power of a Power
For all real numbers b and all positive integers m and n,
(bm)n = bmn
• Try some:
(c7)5
(y3)10
(x3)3
(a21)2
• What about (2x)3 ?
(2x)3 = 2x * 2x * 2x
= (2 * 2 * 2) * (x * x * x)
= 23 * x3 = 8x3
To find the power of a product, raise each factor to that power.
• Power of a Product
For all real numbers a and b and all positive integers,
abm= ambm
• Notice:
Do not confuse (2x)3 and 2x3
(2x)3 means 2x * 2x * 2x
2x3 means 2 * x * x * x
• Try some:
(-4c)3
(-xy2)4
-4x(5x3)2
(-2a4b6)5
• Turn to page 205
Do 1-16