Algebra 1 : How to multiply monomial quotients

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #571 : Variables

Multiply the following monomial quotients:

Possible Answers:

Correct answer:

Explanation:

To solve this problem, split it into two steps:

1. Multiply the coefficients

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

Combine these to get the final answer:

Example Question #572 : Variables

Multiply the following monomial quotients:

Possible Answers:

Correct answer:

Explanation:

To solve this problem, split it into two steps:

1. Multiply the coefficients

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

Example Question #573 : Variables

Simplify the following:

Possible Answers:

Correct answer:

Explanation:

To solve, simply multiply numerators and denominators and then simplify. Thus,

Example Question #574 : Variables

Choose the answer that is equal to .

Possible Answers:

Correct answer:

Explanation:

First multiply 4 and 12 to get the expression

.

Then remember that to multiple like terms with exponents, add the exponents.

This gives the answer, .

Example Question #575 : Variables

Choose the expression that is equal to .

Possible Answers:

Correct answer:

Explanation:

Remember that to multiply like variables with exponents you add the exponents.

This gives .

Also remember that a variable raised to a negative exponential is the same as 1/that same variable to that positive exponential.

For example,  is equivalent to .

This thinking leads to the answer .

Example Question #576 : Variables

Multiply:  

Possible Answers:

Correct answer:

Explanation:

Write out the factors of the second term to see what terms can be cancelled in the numerator and denominator.

After cancellation of common terms, the answer is:  

Example Question #577 : Variables

Simplify the expression . What is the degree of the simplified monomial?

Possible Answers:

Correct answer:

Explanation:

The degree of a monomial term is the sum of its exponents, which here is

.

Example Question #578 : Variables

Simplify the expression . What is the exponent of  ?

Possible Answers:

Correct answer:

Explanation:

The exponent of  is 7.

Example Question #579 : Variables

Simplify: .

What is the exponent of  in the simplified form, and does it appear in the numerator or denominator?

Possible Answers:

1, in the numerator

does not appear in the simplified form of the expression

2, in the denominator

2, in the numerator

1, in the denominator

Correct answer:

1, in the denominator

Explanation:

The exponent of is 1, in the denominator.

Example Question #580 : Variables

Simplify: .

What is the exponent of in the simplified form, and does it appear in the numerator or denominator?

Possible Answers:

1, in the denominator

2, in the denominator

does not appear in the simplified form of the expression

2, in the numerator

1, in the numerator

Correct answer:

2, in the numerator

Explanation:

To simplify this expression use the law of exponents which state that when a term is raised to a power, multiply the exponents. Also, when terms of like bases are divided the exponents are subtracted.

The exponent of is 2, in the numerator.

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