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INSTRUCTORS Carleen Eaton Grant Fraser Eric Smith
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For more information, please see full course syllabus of Algebra 1
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Lecture Comments (5)

1 answer

Last reply by: Dr Carleen Eaton
Sat Jan 16, 2016 10:53 PM

Post by Jessie Carrillo on January 12 at 07:59:30 PM

professor, can you please go step by step in how you got 1/12 for the last part of example 4. I keep getting -9/8a^40b^44c^36

1 answer

Last reply by: Dr Carleen Eaton
Mon Feb 7, 2011 5:16 PM

Post by Matthew Chantry on February 4, 2011

In Example 4, the final constant should be 1/9, not 1/12.

0 answers

Post by S A A Mazeed Sumon on May 2, 2010

Have written 18 in place of 81 in one line of the equation.....

Multiplying Monomials

  • A monomial is a product of a number and zero or more variables. If there are no variables, the monomial is called a constant.
  • A power is an expression of the form xn, where n is a positive integer. The variable x is called the base and the number n is called the exponent.
  • Recall from earlier work the laws of exponents: an· am = am+n, (am)n = amn, and
  • (ab)m = ambm.
  • An expression is considered to be in simplified form if each base is used exactly once, there are no powers of powers, and all fractions are in simplified form.
  • You will often be asked to convert a given expression into simplified form.

Multiplying Monomials

(2a3b5)(6a2b2c4)
  • 12a3 + 2b5 + 2c4
12a5b7c4
(4x7y3)(9x6yz2)
  • 36x7 + 6y3 + 1z
36x13y4z
(5mn3)(6m2n7)
  • 30m1 + 2n3 + 7
30m3n10
(4a4b9c2)3
  • (4)3(a4)3(b9)3(c2)3
  • 64a4 ×3b9 ×3c2 ×3
64a12b27c6
(8x2y3z4)2
  • (8)2(x2)2(y3)2(z4)2
  • 64x2 ×2y3 ×2z4 ×2
64x4y6z8
(5g3h6i)4
  • (5)4(g3)4(h6)4(i)4
  • 625g3 ×4h6 ×4i4
625g12h24i4
(7a2b3c3)2
  • (7)2(a2)2(b3)2(c3)2
  • 49a2 ×2b3 ×2c3 ×2
49a4b6c6
(3g5h3i4)2( − 4g2h6i7)3
  • [(3)2(g5)2(h3)2(i4)2][( − 4)3(g2)3(h6)3(i7)3]
  • 9g10h6i8 ( − 64)g6h18i21
  • (9)( − 64)(g10 ×g6)(h6 ×h18)(i8 ×i21)
  • − 576(g10 + 6)(h6 + 18)(i8 + 21)
- 576g16h24i29
(5g5h6i7)3( − 8g2h3i4)2
  • [(5)3(g5)3(h6)3(i7)3][( − 8)2(g2)2(h3)2(i4)2]
  • 125g15h18i21(64)g4h6i8
  • (125)(64)(g15 ×g4)(h18 ×h6)(i21 ×i8)
  • (125)(64)(g15 + 4)(h18 + 6)(i21 + 8)
8000g19h24i29
( − [1/3]x2y5z6 )2( [5/6]x4y7z3 )3( x5y4 )4
  • ( − [1/3] )2(x2)2(y5)2(z6)2( [5/6] )3(x4)3(y7)3(z3)3(x5)4(y4)4
  • [1/9]( x4y10z12 )[125/216]( x12y21z9 )( x20y16 )
  • [1/9] ×[125/216]( x4 ×x12 ×x20 )( y10 ×y21 ×y16 )( z12 ×z9 )
3000x36y47z21

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

Multiplying Monomials

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • What is a Monomial 0:09
    • Examples
    • Power
    • Base and Exponent
  • Properties of Exponents 2:16
    • Add Exponents
    • Multiply Exponents
    • Product Exponent
  • Simplified Form 7:26
    • Examples
  • Example 1: Simplify the Monomial 8:26
  • Example 2: Simplify the Monomial 10:32
  • Example 3: Simplify the Monomial 12:48
  • Example 4: Simplify the Monomial 17:33