Use the quotient rule to rewrite each expression, then simplify. 30 x 5 y 3 z 3 − 15 x 2 y 3 z \frac{30x^5y^3z^3}{-15x^2y^3z}

this problem, we want to use the quotient rule to rewrite and simplify this expression. 30 times x to the fifth power times y to the third power times z to the third power, all divided by negative 15 times x squared times y to the third power times z. So my first step is I'm going to break apart each of these according to their common bases. So first, we'll break apart our constants as 30 over negative 15, and that will be multiplied by x to the fifth over x squared times y to the third over y to the third times z to the third over z. Now, I can simplify each of these quotients. So first, we know that 30 divided by negative 15 is negative two, x to the fifth divided by x to the second, we can use our quotient rule and subtract our exponents since we have a common base and we'll get x to the third power. Next, y cubed over y cubed will become y to the zeroth power, which is just one. And lastly, z to the third power divided by z is the same as z to the third power divided by z to the first power. So subtracting our exponents, we get z to the second power. And since anything multiplied by one is just the same thing, we can simplify this a little bit more and write this as negative two times x cubed times z squared. And this is our expression now in its simplest form.

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1. Review of Real Numbers2h 43m

Simplifying Fractions
30m

Evaluating Exponents
29m

Evaluating Expressions
15m

Translating Phrases to Expressions
16m

Translating Sentences to Equations
9m

The Distributive Property
17m

Simplifying Expressions
44m

2. Linear Equations and Inequalities5h 35m

Solving Linear Equations
2h 23m

Linear Inequalities in One Variable
46m

Set Operations and Compound Inequalities
1h 7m

Absolute Value Equations
38m

Absolute Value Inequalities
39m

3. Solving Word Problems2h 46m

Introduction to Problem Solving
37m

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25m

Percent Problem Solving
59m

Mixture Problem Solving
43m

4. Graphs and Functions5h 12m

The Rectangular Coordinate System
44m

Graph Linear Equations in Two Variables
24m

Graph Linear Equations Using Intercepts
23m

Slope of a Line
44m

Slope-Intercept Form
38m

Point Slope Form
22m

Linear Inequalities in Two Variables
28m

Introduction to Relations and Functions
53m

Function Notation
15m

Composition of Functions
17m

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29m

Solving Systems of Linear Equations by Substitution
15m

Solving Systems of Linear Equations by Elimination
45m

Systems of Linear Inequalities
23m

6. Exponents, Polynomials, and Polynomial Functions3h 17m

The Product Rule
9m

The Quotient Rule
10m

Intro to the Power Rules
17m

The Power of a Quotient Rule
13m

Negative Exponents
24m

Simplifying Exponential Expressions Using All Exponent Rules
6m

Intro to Polynomials
21m

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20m

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38m

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34m

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38m

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11m

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37m

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41m

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41m

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42m

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25m

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19m

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32m

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32m

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44m

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27m

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47m

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47m

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19m

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53m

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18m

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51m

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25m

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26m

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40m

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1h 28m

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25m

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35m

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33m

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Introduction to Sequences
40m

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27m

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29m

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13m

6. Exponents, Polynomials, and Polynomial Functions

The Quotient Rule

Intermediate Algebra

6. Exponents, Polynomials, and Polynomial Functions

The Quotient Rule

Problema precedenteProssimo problema

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Use the quotient rule to rewrite each expression, then simplify.
$\frac{30 x^{5} y^{3} z^{3}}{- 15 x^{2} y^{3} z}$

$2 x cubed z squared$

$negative 2 x cubed z squared$

$negative 2 x cubed y cubed z squared$

$negative 2 x squared z cubed$

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Problema precedenteProssimo problema

Guida verificata passo dopo passo

Identify the given expression as a quotient of two terms: $\frac{30x^5y^3z^3}{-15x^2y^3z}$.

Apply the quotient rule for exponents, which states that when dividing like bases, subtract the exponents: $\frac{a^m}{a^n} = a^{m-n}$.

Divide the coefficients (numerical parts) separately: divide 30 by -15 to simplify the numerical coefficient.

Subtract the exponents of each variable in the numerator by the corresponding exponents in the denominator: for $x$, $y$, and $z$, calculate $x^{5-2}$, $y^{3-3}$, and $z^{3-1}$ respectively.

Combine the simplified coefficient and variables with their new exponents to write the simplified expression.