Rewrite the expression with NO negative exponents. 1 5 − 3 \frac{1}{5^{-3}}

So, let's look at our next practice problem. We have one divided by five to the negative third power and the problem tells us to rewrite this expression with no negative exponents. Using our new rules, what we see is that when we have negative exponents, whether they're in the top or the bottom of a fraction, we rewrite the reciprocal by flipping the fraction and just rewriting with the positive exponents. So, what we do here is we have one divided by five to the negative third in the denominator. So, what it tells us is we're going to have to move this to the top of the fraction. So what this really just becomes here is five to the positive third power divided by one because that's flipping the fraction over. Now, you could choose to rewrite this like this and this would be perfectly fine, so this would be another answer, or because we just have a one on the bottom, you could just rewrite this as five to the third power. Now, if you have to simplify this further and you're told to simplify this with no exponents at all, we can actually take this five to the third power and we could rewrite this because we know when we have variables raised to exponents, we just leave it alone we can't simplify any further. But, five to the third power actually is a number. So, this is also just written as five times five times five, and if you have to multiply this on the side or if you have a calculator, you'll just see that five times five is 25, 25 times five is 125. So, again, I just want to point out here if you're allowed to just leave this as, exponents, you could just rewrite this as five to the third power, but if you wanted to fully simplify this, you would just actually figure out what that number is and evaluate that, which is 135. Alright, that's all there is to it. Let's move

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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

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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

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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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Set Operations and Compound Inequalities
42m

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38m

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39m

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28m

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23m

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Introduction to Relations and Functions
57m

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15m

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5m

Composition of Functions
24m

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27m

11. Roots, Radicals, and Complex Numbers3h 57m

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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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55m

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32m

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35m

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35m

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41m

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Introduction to Sequences
40m

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27m

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26m

Factorials
11m

6. Exponents and Polynomials

Negative Exponents

Beginning & Intermediate Algebra

6. Exponents and Polynomials

Negative Exponents

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Rewrite the expression with NO negative exponents.
$\frac{1}{5^{- 3}}$

$5 cubed$

$the fraction with numerator 1 and denominator 5 cubed$

$\frac{1}{3^{5}}$

$5^{- 3}$

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Problema precedenteProssimo problema

Guida verificata passo dopo passo

Identify the expression given: $\frac{1}{5^{-3}}$. Notice that the denominator has a negative exponent.

Recall the rule for negative exponents: $a^{-n} = \frac{1}{a^n}$, which means a negative exponent indicates the reciprocal of the base raised to the positive exponent.

Apply this rule to the denominator: $5^{-3} = \frac{1}{5^3}$. So the original expression becomes $\frac{1}{\frac{1}{5^3}}$.

Understand that dividing by a fraction is the same as multiplying by its reciprocal. So, $\frac{1}{\frac{1}{5^3}} = 1 \times 5^3$.

Therefore, the expression with no negative exponents is simply \$5^3$.