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Algebra 1 : Variables

Study concepts, example questions & explanations for Algebra 1

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10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #551 : Variables

Multiply the following monomial quotients:

$6\cdot3x$

Possible Answers:

$18x^{2}$

12x

18x

Correct answer:

18x

Explanation:

To solve this problem, split it into two steps:

1. Multiply the coefficients

$6\cdot3=18$

2. Combine this number with the single variable to get the final answer:

$18\cdot x=18x$

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Example Question #552 : Variables

Multiply the following monomial quotients:

$x^{2}\cdot 5x$

Possible Answers:

$5x^{3}$

$6x^{2}$

$5x^{2}$

$6x^{3}$

Correct answer:

$5x^{3}$

Explanation:

To solve this problem, split it into two steps:

1. Multiply the coefficients

$5\cdot1=5$

2. Multiply the variables. We also need to remember the following laws of exponents rule: When multiplying variables, add the exponents.

$x\cdot x^{2}=x^{1+2}=x^{3}$

Combine these to get the final answer:

$5x^{3}$

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Example Question #553 : Variables

Multiply the following monomial quotients:

$x^{2}\cdot x^{3}$

Possible Answers:

$2x^{5}$

$2x^{6}$

$x^{6}$

$x^{5}$

Correct answer:

$x^{5}$

Explanation:

To solve this problem, split it into two steps:

1. Multiply the coefficients

$1\cdot1=1$

2. Multiply the variables. We also need to remember the following laws of exponents rule: When multiplying variables, add the exponents.

$x^{2}\cdot x^{3}=x^{2+3}=x^{5}$

Combine these to get the final answer:

$x^{5}$

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Example Question #131 : Monomials

Multiply the following monomial quotients:

$6x\cdot 6x$

Possible Answers:

$12x^{2}$

$36x^{2}$

12x

$6x^{2}$

Correct answer:

$36x^{2}$

Explanation:

To solve this problem, split it into two steps:

1. Multiply the coefficients

$6\cdot6=36$

2. Multiply the variables. We also need to remember the following laws of exponents rule: When multiplying variables, add the exponents.

$x\cdot x=x^{1+1}=x^{2}$

Combine these to get the final answer:

$36x^{2}$

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Example Question #131 : Monomials

Multiply the following monomial quotients:

$4x\cdot 5x^{2}$

Possible Answers:

$9x^{3}$

$20x^{3}$

20x

$20x^{2}$

Correct answer:

$20x^{3}$

Explanation:

To solve this problem, split it into two steps:

1. Multiply the coefficients

$4\cdot5=20$

2. Multiply the variables. We also need to remember the following laws of exponents rule: When multiplying variables, add the exponents.

$x\cdot x^{2}=x^{1+2}=x^{3}$

Combine these to get the final answer:

$20x^{3}$

Report an Error

Example Question #132 : Monomials

Multiply the following monomial quotients:

$2x^{4}\cdot 6x$

Possible Answers:

$8x^{5}$

$12x^{5}$

$12x^{4}$

$8x^{4}$

Correct answer:

$12x^{5}$

Explanation:

To solve this problem, split it into two steps:

1. Multiply the coefficients

$2\cdot6=12$

2. Multiply the variables. We also need to remember the following laws of exponents rule: When multiplying variables, add the exponents.

$x^{4}\cdot x=x^{4+1}=x^{5}$

Combine these to get the final answer:

$12x^{5}$

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Example Question #552 : Variables

Multiply the following monomial quotients:

$3x\cdot 2x$

Possible Answers:

$4x^{2}$

$6x^{2}$

Correct answer:

$6x^{2}$

Explanation:

To solve this problem, split it into two steps:

1. Multiply the coefficients

$3\cdot2=6$

2. Multiply the variables. We also need to remember the following laws of exponents rule: When multiplying variables, add the exponents.

$x\cdot x=x^{1+1}=x^{2}$

Combine these to get the final answer:

$6x^{2}$

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Example Question #134 : Monomials

Multiply the following monomial quotients:

$x^{6}\cdot x^{4}$

Possible Answers:

$x^{10}$

$2x^{5}$

$2x^{10}$

$x^{24}$

Correct answer:

$x^{10}$

Explanation:

To solve this problem, split it into two steps:

1. Multiply the coefficients

$1\cdot1=1$

2. Multiply the variables. We also need to remember the following laws of exponents rule: When multiplying variables, add the exponents.

$x^{6}\cdot x^{4}=x^{6+4}=x^{10}$

Combine these to get the final answer:

$x^{10}$

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Example Question #135 : Monomials

Multiply the following monomial quotients:

$2x^{3}\cdot x^{5}=2x^{8}$

Possible Answers:

$2x^{15}$

$3x^{8}$

$4x^{12}$

$2x^{8}$

Correct answer:

$2x^{8}$

Explanation:

To solve this problem, split it into two steps:

1. Multiply the coefficients

$2\cdot1=2$

2. Multiply the variables. We also need to remember the following laws of exponents rule: When multiplying variables, add the exponents.

$x^{3}\cdot x^{5}=x^{3+5}=x^{8}$

Combine these to get the final answer:

$2x^{8}$

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Example Question #136 : Monomials

Multiply the following monomial quotients:

$x^{10}\cdot 3x$

Possible Answers:

$3x^{11}$

$4x^{12}$

$4x^{10}$

$3x^{10}$

Correct answer:

$3x^{11}$

Explanation:

To solve this problem, split it into two steps:

1. Multiply the coefficients

$1\cdot3=3$

2. Multiply the variables. We also need to remember the following laws of exponents rule: When multiplying variables, add the exponents.

$x^{10}\cdot x=x^{10+1}=x^{11}$

Combine these to get the final answer:

$3x^{11}$

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Algebra 1 : Variables

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #551 : Variables

Example Question #552 : Variables

Example Question #553 : Variables

Example Question #131 : Monomials

Example Question #131 : Monomials

Example Question #132 : Monomials

Example Question #552 : Variables

Example Question #134 : Monomials

Example Question #135 : Monomials

Example Question #136 : Monomials

All Algebra 1 Resources

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