Use the product rule to multiply the following.7m24⋅2n4\sqrt[4]{7m^2}\cdot\sqrt[4]{2n}

14m2n4\sqrt[4]{$$14m^2n$$}414m2n

Use the product rule to multiply the following. 7 m 2 4 ⋅ 2 n 4 \sqrt[4]{7m^2}\cdot\sqrt[4]{2n}

we're asked to use the product rule to multiply the following. We have the fourth root of seven m squared times the fourth root of two n. So we're gonna go ahead and apply our product rule in order to condense the product of these two radicals into just one. So rewriting this here, this is going to be the fourth root because remember that's what both of these are. And then doing that multiplication underneath that one radical, this is seven m squared times two n. Doing some further simplification here, we can go ahead and multiply that seven times two to give us 14. So this becomes the fourth root of 14 m squared n, and that's our solution. Having used our product rule for nth roots to do that multiplication. Let us know if you have any questions.

Use the product rule to multiply the following.7m24⋅2n4\sqrt[4]{$$7m^2$$}\cdot\sqrt[4]{2n}

14m2n4\sqrt[4]{$$14m^2n$$}414m2n

7m2+2n4\sqrt[4]{$$7m^2+2n$$}47m2+2n

(14m24)n\left(\sqrt[4]{$$14m^2$$}\right)n(414m2)n

7m24+2n4\sqrt[4]{$$7m^2$$}+\sqrt[4]{2n}47m2+42n

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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

Multiplying Polynomials
33m

Special Products
34m

7. Factoring2h 42m

Factoring by Greatest Common Factor & Grouping
37m

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

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44m

9. Inequalities and Absolute Value2h 52m

Set Operations and Compound Inequalities
42m

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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

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27m

11. Roots, Radicals, and Complex Numbers2h 45m

Introduction to Radical Expressions
24m

Simplifying Radical Expressions
27m

Adding and Subtracting Radicals
19m

Multiplying, Dividing, and Rationalizing Radicals
23m

Introduction to Complex Numbers
18m

Multiplying and Dividing Complex Numbers
51m

12. Quadratic Equations and Functions3h 1m

The Square Root Property
25m

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26m

The Quadratic Formula
40m

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1h 28m

13. Inverse, Exponential, & Logarithmic Functions1h 5m

Introduction to Inverse Functions
25m

Exponential Functions
13m

Introduction to Logarithmic Functions
26m

14. Conic Sections & Systems of Nonlinear Equations58m

Graphing Circles
32m

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15m

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10m

15. Sequences, Series, and the Binomial Theorem1h 46m

Introduction to Sequences
40m

Arithmetic Sequences
27m

Geometric Sequences
26m

Factorials
11m

11. Roots, Radicals, and Complex Numbers

Simplifying Radical Expressions

Beginning & Intermediate Algebra

11. Roots, Radicals, and Complex Numbers

Simplifying Radical Expressions

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Multiple Choice

Use the product rule to multiply the following.
$\sqrt[4]{7 m^{2}} \cdot \sqrt[4]{2 n}$

$$\sqrt$[4]{7m^2+2n}$

$$\sqrt$[4]{14m^2n}$

$$\left$($\sqrt$[4]{14m^2}$\right$)n$

$$\sqrt$[4]{7m^2}+$\sqrt$[4]{2n}$

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Verified step by step guidance

Identify the expression to multiply: $\sqrt[4]{7m^{2}} \cdot \sqrt[4]{2n}$.

Recall the product rule for radicals with the same index: $\sqrt[n]{a} \cdot \sqrt[n]{b} = \sqrt[n]{a \cdot b}$.

Apply the product rule by multiplying the radicands (the expressions inside the roots): $7m^{2} \times 2n = 14m^{2}n$.

Rewrite the product under a single fourth root: $\sqrt[4]{14m^{2}n}$.

This expression represents the simplified product of the original radicals using the product rule.

1:05m

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Struggling with Beginning & Intermediate Algebra?

Use the product rule to multiply the following.7m24⋅2n4\(\sqrt\)[4]{7m^2}\(\cdot\]\sqrt\)[4]{2n}

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Use the product rule to multiply the following.
$\sqrt[4]{7 m^{2}} \cdot \sqrt[4]{2 n}$