How to divide monomial quotients

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Algebra › How to divide monomial quotients

Questions 1 - 10
1

Simplify the expression.

Explanation

Because we are only multiplying terms in the numerator, we can disregard the parentheses.

To combine like terms in the numerator, we add their exponents.

To combine like terms between the numerator and denominator, subtract the denominator exponent from the numerator exponent.

Remember that any negative exponents stay in the denominator.

2

Divide the following monomial quotients:

Explanation

To solve this problem, split it into two steps:

1. Divide the coefficients

2. Divide the variables. We also need to remember the following laws of exponents rule: When dividing variables, subtract the exponents.

Combine these to get the final answer:

3

Evaluate:

Explanation

To evaluate, we must cancel out like values on the numerator and denominator:

4

Simplify the following:

Explanation

First, flip the numerator and the denominator of the second fraction to turn the division into multiplication.

We can then cancel like terms.

From both the numerator and denominator, remove one , remove one , and remove one :

Then we finish by multiplying the constants:

5

Find the quotient of the following

.

Explanation

When dividing polynomials, you subtract the powers with the same base.

We know that anything raised to the zero power equals 1.

So we get

We simplify the integers.

We get

6

Find the result of

.

Explanation

The question asks for the quotient of .

We can rewrite the expression using the rules of multiplication and exponents to find the answer of .

7

Simplify the rational expression.

Explanation

To simplify variables with exponents through division, you must subtract the exponent in the denominator from the numerator.

Remember that negative exponents will eventually be moved back to the denominator.

8

Simplify

Explanation

Rewrite so that you are multiplying the reciprocal of the second fraction:

You can then simplify using rules of exponents:

9

Simplify:

Explanation

and cancel out, leaving in the numerator. 5 and 25 cancel out, leaving 5 in the denominator

10

Divide:

Explanation

Write out the factors for the numerator and denominator.

Cancel the common factors on the top and bottom.

The answer is:

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