What is the difference between dividing monomials and multiplying monomials

While dividing monomials with exponents , we need to consider exponents' rules. Thus, in the case of the division of monomials, then their base is the same, just subtract the exponents.

It's the opposite of the multiplication rule. Now, in the above case, the monomials have only one term each consisting of the same variable or same base, that is y. Dividing monomials with negative exponents is almost the same as multiplying them. In the case of multiplying monomials, we used to add the powers but in the case of dividing monomials, we need to subtract.

If the bases are the same, subtract the exponents. Note that you need to flip the exponent and make it positive if needed. If both the monomials have negative coefficients, the negative signs cancel out and the answer so obtained will be having a positive coefficient only.

Consider the two monomials, x 2 and 7x. In case, there is a negative sign with even one of the monomials, the answer will have a negative sign too. Consider the two monomials, x and -7x.

Check out these interesting articles to learn more about dividing monomials and its related topics. Dividing monomials refers to the method of dividing monomials by expressing the terms of the two given expressions in their expanded form and then canceling out the common ones. Clearly, dividing polynomials follow the same procedure as multiplication of monomials following the different exponent rule.

As we already know that the variables of a monomial cannot have a negative or fractional exponent, whereas the dividing monomials with negative coefficients follow the rules as given below:. Divide coefficients, and divide the variables by subtracting the exponents of each x term.

Sometimes division requires simplification. Simplify to. Divide the variables by subtracting the exponents of r. Note that the variable has a negative exponent. Simplify by rewriting it as the inverse of r. Remember that a term is not considered simplified if it contains a negative exponent; this is why was rewritten as. A 11x 4. You divided 22 by 2, but you must subtract the exponents of the variable x. The correct answer is 11 x 3.

You correctly divided the variables, but you must also divide 22 by 2. Divide the variables by subtracting the exponents. Dividing Polynomials by Monomials. The distributive property states that you can distribute a factor that is being multiplied by a sum or difference, and likewise you can distribute a divisor that is being divided into a sum or difference as division can be changed to multiplication.

Or you can distribute the 2, and divide each term by 2. Distribute 2 x over the polynomial by dividing each term by 2 x. Divide each term, a monomial divided by another monomial. If a monomial is raised to a power, it can be simplified with a single exponent. Similarly, 3y 2 z 4 can be simplified as 3 4 y 2 4 z 4 or 81y 8 z 4.

The general rule in algebraic terms is that x a b means x ab. Also, xy a means the same thing as x a y a , even when the monomial itself has a number of factors.

If there are exponents in the numerator and the denominator, the exponents must be the same in order to simplify the expression. One half of 4 is 2, and by the definition of multiplying exponents with the same base, x 3 x -2 is the same thing as x or x 1 , or 2x. Interested in algebra tutoring services? Learn more about how we are assisting thousands of students each academic year.

SchoolTutoring Academy is the premier educational services company for K and college students. We offer tutoring programs for students in K, AP classes, and college. Login Get started. Deborah February 13, No Comments.