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## Practice Questions

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## Table of Contents

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### 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 x^{n}, 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: a
^{n}· a^{m}= a^{m+n}, (a^{m})^{n}= a^{mn}, and - (ab)
^{m}= a^{m}b^{m}. - 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

(2a

^{3}b^{5})(6a^{2}b^{2}c^{4})- 12a
^{3 + 2}b^{5 + 2}c^{4}

12a

^{5}b^{7}c^{4}(4x

^{7}y^{3})(9x^{6}yz^{2})- 36x
^{7 + 6}y^{3 + 1}z

36x

^{13}y^{4}z(5mn

^{3})(6m^{2}n^{7})- 30m
^{1 + 2}n^{3 + 7}

30m

^{3}n^{10}(4a

^{4}b^{9}c^{2})^{3}- (4)
^{3}(a^{4})^{3}(b^{9})^{3}(c^{2})^{3} - 64a
^{4 ×3}b^{9 ×3}c^{2 ×3}

64a

^{12}b^{27}c^{6}(8x

^{2}y^{3}z^{4})^{2}- (8)
^{2}(x^{2})^{2}(y^{3})^{2}(z^{4})^{2} - 64x
^{2 ×2}y^{3 ×2}z^{4 ×2}

64x

^{4}y^{6}z^{8}(5g

^{3}h^{6}i)^{4}- (5)
^{4}(g^{3})^{4}(h^{6})^{4}(i)^{4} - 625g
^{3 ×4}h^{6 ×4}i^{4}

625g

^{12}h^{24}i^{4}(7a

^{2}b^{3}c^{3})^{2}- (7)
^{2}(a^{2})^{2}(b^{3})^{2}(c^{3})^{2} - 49a
^{2 ×2}b^{3 ×2}c^{3 ×2}

49a

^{4}b^{6}c^{6}(3g

^{5}h^{3}i^{4})^{2}( − 4g^{2}h^{6}i^{7})^{3}- [(3)
^{2}(g^{5})^{2}(h^{3})^{2}(i^{4})^{2}][( − 4)^{3}(g^{2})^{3}(h^{6})^{3}(i^{7})^{3}] - 9g
^{10}h^{6}i^{8}( − 64)g^{6}h^{18}i^{21} - (9)( − 64)(g
^{10}×g^{6})(h^{6}×h^{18})(i^{8}×i^{21}) - − 576(g
^{10 + 6})(h^{6 + 18})(i^{8 + 21})

- 576g

^{16}h^{24}i^{29}(5g

^{5}h^{6}i^{7})^{3}( − 8g^{2}h^{3}i^{4})^{2}- [(5)
^{3}(g^{5})^{3}(h^{6})^{3}(i^{7})^{3}][( − 8)^{2}(g^{2})^{2}(h^{3})^{2}(i^{4})^{2}] - 125g
^{15}h^{18}i^{21}(64)g^{4}h^{6}i^{8} - (125)(64)(g
^{15}×g^{4})(h^{18}×h^{6})(i^{21}×i^{8}) - (125)(64)(g
^{15 + 4})(h^{18 + 6})(i^{21 + 8})

8000g

^{19}h^{24}i^{29}( − [1/3]x

^{2}y^{5}z^{6})^{2}( [5/6]x^{4}y^{7}z^{3})^{3}( x^{5}y^{4})^{4}- ( − [1/3] )
^{2}(x^{2})^{2}(y^{5})^{2}(z^{6})^{2}( [5/6] )^{3}(x^{4})^{3}(y^{7})^{3}(z^{3})^{3}(x^{5})^{4}(y^{4})^{4} - [1/9]( x
^{4}y^{10}z^{12})[125/216]( x^{12}y^{21}z^{9})( x^{20}y^{16}) - [1/9] ×[125/216]( x
^{4}×x^{12}×x^{20})( y^{10}×y^{21}×y^{16})( z^{12}×z^{9})

3000x

^{36}y^{47}z^{21}*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

1 answer

Last reply by: Dr Carleen Eaton

Wed Jul 12, 2017 11:06 PM

Post by Ling Huang on June 6, 2017

Shouldn't the final constant be 16/81 multiplied by 27/64?

1 answer

Last reply by: Dr Carleen Eaton

Sat Jan 16, 2016 10:53 PM

Post by Jessie Carrillo on January 12, 2016

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.....