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7.1 Multiplying Monomials. Monomial - a number, a variable or a product of a number and one or more variables. Monomials do not have variables in the denominator . A real number is a monomial called a constant. Example 1 – Determine whether the following expressions are monomials. a. 10. - PowerPoint PPT Presentation
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7.1 Multiplying Monomials
Monomial - a number, a variable or a product of a number and one or more variables.
xyayExamples
4,3,,7:
Monomials do not have variables in the denominator.
A real number is a monomial called a constant.
Example 1 – Determine whether the following expressions are monomials.
a. 10 yes, this is an example of a constant
b. x + y no, this expression involves the addition not the product of variables
c. x yes, a single variable is a monomial
d.x3 no, cannot have variables in the
denominator
Fill out Frayer Model with your partner
Monomials
Definition Characteristics
Examples Non-examples
Homework p. 361 14-19
A number or variable with an exponent is called a power.
23 3 is the base; 2 is the exponent 3x x is the base; 3 is the exponent
7.1 Multiplying Monomials (Day 2)
The exponent tells you how many times to use the base as a factor.
3x xxx
Rules of Exponents:
1. Product of Powers: when multiplying powers with like bases add exponents.
53232 xorxxx
Example 1 – Simplify
))()()()(1)(3())(3( 342342 yyxxyxyx Group coefficients and variables
))()(13( 3142 yx Product of Powers463 yx Simplify
3423 yxyx
Try - Simplify:
)6)(4( 6357 yxyx
))()()()(6)(4( 6537 yyxx))()(64( 6537 yx
111024 yx
Rules of Exponents:
2. Power of a Power: to find the power of a power multiply exponents.
63232)( xorxx
Example 2 – Simplify
232 ])2[(232 )2(
26 )2()2( 26
122096,4
Try 242 ])3[(
)3( 242 163
721,046,43
Rules of Exponents:
3. Power of a Product: to find the power of a product find the power of each factor and multiply.
333333 27)3()3( yxoryxxy
Example 3 – Simplify
3)5( ab333)5( ba
33125 ba
Try2)4( xy
222)4( yx
2216 yx
Homework:
Page 361 20 - 28
7.1 Multiplying Monomials Day 3
Simplifying Monomial Expressions:
Each base appears exactly once,
There are no powers of powers, and
All fractions are in simplest form
Example 1: Simplify 452243 )2(])8[( ghhg
45443 )2()8( ghhg
2041612 )16()096,4( hghg
454444434 )()2()()()8( hghg
2016412)16)(4096( hhgg3616536,65 hg
Try:23343 )3()2( vwwv
232234333 )()3()()()2( wvwv 62129 )9(8 wvwv61229)9)(8( wwvv
181172 wv
Do the online Self-Check Quiz for 7.1 with your partner. When you complete the quiz click the “check it” button. Fill in the boxes to e-mail results.Your Name: partner’s namesYour E-mail Address: AlgebraE-mail results to: [email protected]
Homework:
Page 362 31 – 34, 39 & 40
