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Algebra 1 : How to divide monomial quotients

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Example Question #105 : Monomials

Divide the monomials: $\frac{3x^6yz^3}{3x^{-6}y^6z^5}$

Possible Answers:

$\frac{x^{12}}{y^5z^2}$

$\frac{y^5}{z^2}$

y^5z^2

$\frac{1}{y^5z^2}$

Correct answer:

$\frac{x^{12}}{y^5z^2}$

Explanation:

When powers of a similar base are divided, the powers can be subtracted.

The coefficients will cancel.

Subtract each power for each variable.

$x^{6-(-6)}=x^{12}$

$y^{1-6}= y^{-5} = \frac{1}{y^5}$

$z^{3-5}= z^{-2} = \frac{1}{z^2}$

Multiply and combine each of these terms together.

$x^{12} \times \frac{1}{y^5} \times \frac{1}{z^2}$

The answer is: $\frac{x^{12}}{y^5z^2}$

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Example Question #106 : Monomials

Divide: $\frac{9ab^6}{36a^3b^6}$

Possible Answers:

$\frac{1}{27a^2}$

$\textup{Cannot be solved.}$

$\frac{1}{4a^2}$

4a^2

Correct answer:

$\frac{1}{4a^2}$

Explanation:

Rewrite the numerator and denominator in factors.

$\frac{9ab^6}{36a^3b^6} = \frac{9\times a \times b^6}{9 \times 4 \times a\times a^2 \times b^6}$

Cancel out the common terms in the numerator and denominator. Since all the terms in the numerator cancels out, the numerator becomes a one.

The answer is: $\frac{1}{4a^2}$

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Example Question #107 : Monomials

Simplify the following expression:

Which of the following expressions is equivalent to this one:

$\frac{4a^{3}b^{2}}{6a}\cdot\frac{8c^{4}b^{3}}{2b}$

Possible Answers:

$\frac{16a^2b^3c^4}{3}$

$\frac{8a^{2}b^{4}c^{4}}{3}$

$\frac{8a^{2}b^{3}c^{4}}{3}$

$\frac{32a^3b^3 c^4}{12}$

$\frac{8a^2bc^4}{6}$

Correct answer:

$\frac{8a^{2}b^{4}c^{4}}{3}$

Explanation:

First, simplify each term individually. Let's start with the term on the left. We can factor out from both the numerator and denominator.

$\frac{4a^{3}b^{2}}{6a}\rightarrow \frac{2a^2b^2}{3}$

Next, factor out from the numerator and denominator of the term on the right.

$\frac{8c^{4}b^{3}}{2b}\rightarrow \frac{4c^4b^2}{1}$

Combine and multiply. Remember that when we are multiplying terms with exponents, we need to add their exponential values. Likewise, when we divide exponents, we will subtract their exponential values.

$\frac{4a^3b^2}{6a}\cdot\frac{8c^4b^3}{2b} = \frac{2a^2b^2}{3}\cdot\frac{4c^4b^2}{1}$

$\frac{2a^2b^2}{3}\cdot\frac{4c^4b^2}{1}=\frac{(2a^2b^2)(4c^4b^2)}{3}$

Simplify.

$\frac{(2a^2b^2)(4c^4b^2)}{3}=\frac{8a^2b^4c^4}{3}$

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Algebra 1 : How to divide monomial quotients

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #105 : Monomials

Example Question #106 : Monomials

Example Question #107 : Monomials

All Algebra 1 Resources

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