Simplify the expressions using the quotient to a power property. ( a − 3 ) 4 \left(\frac{a}{-3}\right)^4

Folks. So we have a very similar problem here, but there's one catch. We have a negative sign inside of our parentheses. We're still gonna simplify this expression by using the quotient to a power or the power of a quotient rule. Let's get started here. We're gonna take this four and distribute it to the both the numerator and the denominator. And so on the top, we're just gonna get a to the fourth power. You can't really simplify that any further. But on the bottom here, it's very, very important that you pay attention to this negative sign. We're distributing a four exponent to a bottom or a denominator of negative three. So it's very important that when you distribute this, you keep that negative sign inside the parenthesis. As we've seen before, whenever you have a term that has a negative sign that gets raised to a power, the sign will alternate based on whether the power is odd or even. So it's very, very important that you keep this in mind. So again, on the top, we can't really simplify this because yet we just have a variable to raise to an exponent. But on the bottom, we can simplify this further because this is a number raised to an exponent. If you write this out, we have eight to the fourth divided by negative three times itself four times. So if you don't really know how to deal with this negative sign, you can always just write this out to see how the negatives are gonna work out, or you can just use the rule that when you have a negative raised to an even power, the negative will cancel out. Why? Because if you take negative three times negative three, the negative goes away and it just becomes nine. And then if you have negative three times negative three again, the negative also goes away. And so it's basically like you just have nine times nine, the negatives just completely go away. And so if we simplify this one step further, this is basically like a to the fourth power divided by nine times nine. And so our final expression here is a to the fourth over 81. Just be really, really careful here. If you know the rule that if you have an even power for a negative term, the negative goes away. That's fine. Otherwise, you should just write it up and just see that the negative will just cancel itself out. Alright. So this is our final expression here, a to the fourth over 81, and we can't simplify this any further. Thanks for watching. I'll see you in the next one.

Indice

Skip topic navigation

1. Review of Real Numbers2h 39m

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
40m

2. Linear Equations and Inequalities3h 38m

The Addition and Subtraction Properties of Equality
41m

The Multiplication and Division Properties of Equality
30m

Solving Linear Equations
1h 14m

Linear Inequalities in One Variable
1h 11m

3. Solving Word Problems2h 43m

Introduction to Problem Solving
37m

Formulas
21m

Percent Problem Solving
59m

Mixture Problem Solving
43m

4. Graphing Linear Equations in Two Variables3h 17m

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

5. Systems of Linear Equations1h 43m

Solving Systems of Linear Equations by Graphing
41m

Solving Systems of Linear Equations by Substitution
15m

Solving Systems of Linear Equations by Elimination
45m

6. Exponents and Polynomials3h 25m

The Product Rule
10m

The Quotient Rule
13m

Intro to the Power Rules
18m

The Power of a Quotient Rule
18m

Negative Exponents
28m

Simplifying Exponential Expressions Using All Exponent Rules
6m

Intro to Polynomials
21m

Adding and Subtracting Polynomials
20m

Multiplying Polynomials
33m

Special Products
34m

7. Factoring2h 42m

Factoring by Greatest Common Factor & Grouping
38m

Factoring Trinomials of the Form x² + bx + c
11m

Factoring Trinomials of the Form ax² + bx + c
37m

Factoring Special Products
33m

Quadratic Equations & Applications
41m

8. Rational Expressions and Equations3h 13m

Simplifying Rational Expressions
39m

Multiplying and Dividing Rational Expressions
25m

Adding and Subtracting Rational Expressions with Common Denominators
19m

Least Common Denominators
32m

Adding and Subtracting Rational Expressions with Different Denominators
32m

Rational Equations
44m

9. Inequalities and Absolute Value2h 52m

Set Operations and Compound Inequalities
42m

Absolute Value Equations
38m

Absolute Value Inequalities
39m

Linear Inequalities in Two Variables
28m

Systems of Linear Inequalities
23m

10. Relations and Functions2h 9m

Introduction to Relations and Functions
57m

Function Notation
15m

Graphing Common Functions
5m

Composition of Functions
24m

Direct & Inverse Variation
27m

11. Roots, Radicals, and Complex Numbers3h 57m

Introduction to Radical Expressions
47m

Simplifying Radical Expressions
47m

Adding and Subtracting Radicals
19m

Multiplying, Dividing, and Rationalizing Radicals
53m

Introduction to Complex Numbers
18m

Multiplying and Dividing Complex Numbers
51m

12. Quadratic Equations and Functions3h 1m

The Square Root Property
25m

Completing the Square
26m

The Quadratic Formula
40m

Graphing Quadratic Equations
1h 28m

13. Inverse, Exponential, & Logarithmic Functions2h 31m

Introduction to Inverse Functions
25m

Exponential Functions
35m

Introduction to Logarithmic Functions
33m

Properties of Logarithms
55m

14. Conic Sections & Systems of Nonlinear Equations2h 24m

Graphing Circles
32m

Ellipses
35m

Parabolas
35m

Hyperbolas
41m

15. Sequences, Series, and the Binomial Theorem1h 45m

Introduction to Sequences
40m

Arithmetic Sequences
27m

Geometric Sequences
26m

Factorials
11m

6. Exponents and Polynomials

The Power of a Quotient Rule

Beginning & Intermediate Algebra

6. Exponents and Polynomials

The Power of a Quotient Rule

Problema precedenteProssimo problema

Difficoltà con Beginning & Intermediate Algebra?

Unisciti a migliaia di studenti che si affidano a noi per superare al meglio i loro esami!

Scelta multipla

Simplify the expressions using the quotient to a power property.
${(\frac{a}{- 3})}^{4}$

$\frac{a^{4}}{- 81}$

$\frac{a^{4}}{81}$

$a over 81$

$- \frac{4}{3} a$

0 Commenti

Problema precedenteProssimo problema

Guida verificata passo dopo passo

Identify the expression to simplify: $\left(\frac{a}{-3}\right)^4$.

Apply the quotient to a power property, which states that $\left(\frac{x}{y}\right)^n = \frac{x^n}{y^n}$, so rewrite the expression as $\frac{a^4}{(-3)^4}$.

Calculate the denominator by raising $-3$ to the 4th power: $(-3)^4 = (-3) \times (-3) \times (-3) \times (-3)$.

Since an even power of a negative number results in a positive number, simplify $(-3)^4$ to a positive value.

Write the simplified expression as $\frac{a^4}{81}$, noting that the negative sign disappears because of the even exponent.