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Algebra 1 : Variables

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #4782 : Algebra 1

Multiply the following monomial quotients:

$6\cdot3x$ $\displaystyle 6\cdot3x$

Possible Answers:

$18x^{2}$ $\displaystyle 18x^{2}$

$\displaystyle 9x$

18x $\displaystyle 18x$

12x $\displaystyle 12x$

Correct answer:

18x $\displaystyle 18x$

Explanation:

To solve this problem, split it into two steps:

1. Multiply the coefficients

$6\cdot3=18$ $\displaystyle 6\cdot3=18$

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

$18\cdot x=18x$ $\displaystyle 18\cdot x=18x$

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Example Question #22 : How To Multiply Monomial Quotients

Multiply the following monomial quotients:

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

Possible Answers:

$6x^{2}$ $\displaystyle 6x^{2}$

$5x^{3}$ $\displaystyle 5x^{3}$

$5x^{2}$ $\displaystyle 5x^{2}$

$6x^{3}$ $\displaystyle 6x^{3}$

Correct answer:

$5x^{3}$ $\displaystyle 5x^{3}$

Explanation:

To solve this problem, split it into two steps:

1. Multiply the coefficients

$5\cdot1=5$ $\displaystyle 5\cdot1=5$

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

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

Combine these to get the final answer:

$5x^{3}$ $\displaystyle 5x^{3}$

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Example Question #22 : How To Multiply Monomial Quotients

Multiply the following monomial quotients:

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

Possible Answers:

$2x^{5}$ $\displaystyle 2x^{5}$

$x^{6}$ $\displaystyle x^{6}$

$2x^{6}$ $\displaystyle 2x^{6}$

$x^{5}$ $\displaystyle x^{5}$

Correct answer:

$x^{5}$ $\displaystyle x^{5}$

Explanation:

To solve this problem, split it into two steps:

1. Multiply the coefficients

$1\cdot1=1$ $\displaystyle 1\cdot1=1$

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

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

Combine these to get the final answer:

$x^{5}$ $\displaystyle x^{5}$

Report an Error

Example Question #4783 : Algebra 1

Multiply the following monomial quotients:

$6x\cdot 6x$ $\displaystyle 6x\cdot 6x$

Possible Answers:

$36x^{2}$ $\displaystyle 36x^{2}$

12x $\displaystyle 12x$

$6x^{2}$ $\displaystyle 6x^{2}$

$12x^{2}$ $\displaystyle 12x^{2}$

Correct answer:

$36x^{2}$ $\displaystyle 36x^{2}$

Explanation:

To solve this problem, split it into two steps:

1. Multiply the coefficients

$6\cdot6=36$ $\displaystyle 6\cdot6=36$

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

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

Combine these to get the final answer:

$36x^{2}$ $\displaystyle 36x^{2}$

Report an Error

Example Question #23 : How To Multiply Monomial Quotients

Multiply the following monomial quotients:

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

Possible Answers:

$20x^{2}$ $\displaystyle 20x^{2}$

20x $\displaystyle 20x$

$20x^{3}$ $\displaystyle 20x^{3}$

$9x^{3}$ $\displaystyle 9x^{3}$

Correct answer:

$20x^{3}$ $\displaystyle 20x^{3}$

Explanation:

To solve this problem, split it into two steps:

1. Multiply the coefficients

$4\cdot5=20$ $\displaystyle 4\cdot5=20$

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

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

Combine these to get the final answer:

$20x^{3}$ $\displaystyle 20x^{3}$

Report an Error

Example Question #21 : How To Multiply Monomial Quotients

Multiply the following monomial quotients:

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

Possible Answers:

$8x^{4}$ $\displaystyle 8x^{4}$

$8x^{5}$ $\displaystyle 8x^{5}$

$12x^{5}$ $\displaystyle 12x^{5}$

$12x^{4}$ $\displaystyle 12x^{4}$

Correct answer:

$12x^{5}$ $\displaystyle 12x^{5}$

Explanation:

To solve this problem, split it into two steps:

1. Multiply the coefficients

$2\cdot6=12$ $\displaystyle 2\cdot6=12$

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

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

Combine these to get the final answer:

$12x^{5}$ $\displaystyle 12x^{5}$

Report an Error

Example Question #4784 : Algebra 1

Multiply the following monomial quotients:

$3x\cdot 2x$ $\displaystyle 3x\cdot 2x$

Possible Answers:

$4x^{2}$ $\displaystyle 4x^{2}$

$\displaystyle 5x$

$6x^{2}$ $\displaystyle 6x^{2}$

$\displaystyle 6x$

Correct answer:

$6x^{2}$ $\displaystyle 6x^{2}$

Explanation:

To solve this problem, split it into two steps:

1. Multiply the coefficients

$3\cdot2=6$ $\displaystyle 3\cdot2=6$

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

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

Combine these to get the final answer:

$6x^{2}$ $\displaystyle 6x^{2}$

Report an Error

Example Question #25 : How To Multiply Monomial Quotients

Multiply the following monomial quotients:

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

Possible Answers:

$2x^{5}$ $\displaystyle 2x^{5}$

$x^{24}$ $\displaystyle x^{24}$

$2x^{10}$ $\displaystyle 2x^{10}$

$x^{10}$ $\displaystyle x^{10}$

Correct answer:

$x^{10}$ $\displaystyle x^{10}$

Explanation:

To solve this problem, split it into two steps:

1. Multiply the coefficients

$1\cdot1=1$ $\displaystyle 1\cdot1=1$

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

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

Combine these to get the final answer:

$x^{10}$ $\displaystyle x^{10}$

Report an Error

Example Question #26 : How To Multiply Monomial Quotients

Multiply the following monomial quotients:

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

Possible Answers:

$3x^{8}$ $\displaystyle 3x^{8}$

$4x^{12}$ $\displaystyle 4x^{12}$

$2x^{8}$ $\displaystyle 2x^{8}$

$2x^{15}$ $\displaystyle 2x^{15}$

Correct answer:

$2x^{8}$ $\displaystyle 2x^{8}$

Explanation:

To solve this problem, split it into two steps:

1. Multiply the coefficients

$2\cdot1=2$ $\displaystyle 2\cdot1=2$

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

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

Combine these to get the final answer:

$2x^{8}$ $\displaystyle 2x^{8}$

Report an Error

Example Question #24 : How To Multiply Monomial Quotients

Multiply the following monomial quotients:

$x^{10}\cdot 3x$ $\displaystyle x^{10}\cdot 3x$

Possible Answers:

$4x^{10}$ $\displaystyle 4x^{10}$

$4x^{12}$ $\displaystyle 4x^{12}$

$3x^{10}$ $\displaystyle 3x^{10}$

$3x^{11}$ $\displaystyle 3x^{11}$

Correct answer:

$3x^{11}$ $\displaystyle 3x^{11}$

Explanation:

To solve this problem, split it into two steps:

1. Multiply the coefficients

$1\cdot3=3$ $\displaystyle 1\cdot3=3$

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

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

Combine these to get the final answer:

$3x^{11}$ $\displaystyle 3x^{11}$

Report an Error

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Algebra 1 : Variables

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #4782 : Algebra 1

Example Question #22 : How To Multiply Monomial Quotients

Example Question #22 : How To Multiply Monomial Quotients

Example Question #4783 : Algebra 1

Example Question #23 : How To Multiply Monomial Quotients

Example Question #21 : How To Multiply Monomial Quotients

Example Question #4784 : Algebra 1

Example Question #25 : How To Multiply Monomial Quotients

Example Question #26 : How To Multiply Monomial Quotients

Example Question #24 : How To Multiply Monomial Quotients

All Algebra 1 Resources

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