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Notes

Problems & Videos

$\mathbf{\text{1)}}$ ${\displaystyle \frac{12x^4{y}^{3}z}{3x^2{z}^{4}x}}$

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The answer is $4x{y}^3{z}^{-3}$ or ${\displaystyle \frac{4x{y}^3}{z^3}}$

$\mathbf{\text{2)}}$ ${\displaystyle {\left(\frac{3x}{y}\right)}^2}$

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The answer is ${\displaystyle \frac{9x^2}{y^2}}$

$\mathbf{\text{3)}}$ ${\displaystyle \frac{4x^4{y}^{-2}z}{6x^{-1}yz}}$

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The answer is ${\displaystyle \frac{2x^5}{3y^3}}$ or ${\displaystyle \frac{2}{3}{x}^5{y}^{-3}}$

$\mathbf{\text{4)}}$ ${\displaystyle {\left(\frac{5x^5{y}^{-3}{z}^2}{6x^{-2}yz}\right)}^{-2}}$

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The answer is ${\displaystyle \frac{36y^8}{25x^{14}{z}^2}}$

$\mathbf{\text{5)}}$ ${\displaystyle \frac{5x^6{y}^2{z}^2}{10x^{-2}{z}^4{x}^3}}$

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

See Related Pages

$\bullet \text{ Multiply Monomials}$
$(7m^2{k}^5)(8m^3{k}^4)\dots$

$\bullet \text{ Dividing Monomials}$
${\displaystyle \frac{12x^4{y}^{3}z}{3x^2{z}^{4}x}\dots }$

$\bullet \text{ Adding and Subtracting Polynomials}$
$(4d+7)-(2d-5)\dots$

$\bullet \text{ Multiplying Polynomials}$
$(x+2)(x^2+3x-5)\dots$

$\bullet \text{ Dividing Polynomials}$
$(x^3-8)÷(x-2)\dots$

$\bullet \text{ Dividing Polynomials (Synthetic Division)}$
$(x^3-8)÷(x-2)\dots$

$\bullet \text{ Synthetic Substitution}$
$f(x)=4x^4-3x^2+8x-2\dots$

$\bullet \text{ End Behavior}$
$\text{As }x\to \mathrm{\infty },f(x)\to \mathrm{\infty }$
$\text{As }x\to -\mathrm{\infty },f(x)\to \mathrm{\infty }\dots$

$\bullet \text{ Completing the Square}$
$x^2+10x-24=0\dots$

$\bullet \text{ Quadratic Formula and the Discriminant}$
$x=-b\pm {\displaystyle \frac{\sqrt{b^2-4ac}}{2a}\dots }$

$\bullet \text{ Complex Numbers}$
$i=\sqrt{-1}\dots$

$\bullet \text{ Multiplicity of Roots}$
$$$\dots$

$\bullet \text{ Rational Zero Theorem}$
$\pm 1,\pm 2,\pm 3,\pm 4,\pm 6,\pm 12\dots$

$\bullet \text{ Descartes Rule of Signs}$
$$

$\bullet \text{ Roots and Zeroes}$
$\text{Solve for }x.3x^2+4x=0\dots$

$\bullet \text{ Linear Factored Form}$
$f(x)=(x+4)(x+1)(x-3)\dots$

$\bullet \text{ Polynomial Inequalities}$
$x^3-4x^2-4x+16>0\dots$

$\bullet \text{ Andymath Homepage}$

In Summary

Dividing monomials involves dividing two or more algebraic expressions that each consist of a single term. This process involves dividing the numerical coefficients and the variables, and simplifying the resulting expression as necessary. Dividing monomials is typically taught in an algebra or pre-algebra class. Related topics include factoring, simplifying algebraic expressions, and solving equations.

About Andymath.com

Andymath.com is a free math website with the mission of helping students, teachers and tutors find helpful notes, useful sample problems with answers including step by step solutions, and other related materials to supplement classroom learning. If you have any requests for additional content, please contact Andy at tutoring@andymath.com. He will promptly add the content.

Topics cover Elementary Math, Middle School, Algebra, Geometry, Algebra 2/Pre-calculus/Trig, Calculus and Probability/Statistics. In the future, I hope to add Physics and Linear Algebra content.

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