Simplify each expression. ( − 5 a 2 ) ( 3 a 8 ) (-5a^2)(3a^8)

For this problem, we want to simplify our expression negative five a squared times three a to the eighth power using our product rule. So first, I'm going to go ahead and split some things apart, that way we can group our like factors. So doing this, we're going to rearrange this and group negative five times three, since these are both constants. And we're also going to group a squared by a to the eighth power, since these are like factors and have a common base value of a. Now we can go ahead and combine our constants and use our product rule to combine our variables. So combining our constants, we have negative five times three, which is negative 15. And combining our variables, we have a squared times a to the eighth power. And since these have a common base, we can use our product rule and add the exponents. So we get negative 15 times a to the tenth power. And this is our exponential expression now in its simplest form.

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1. Review of Real Numbers1h 33m

Evaluating Exponents
15m

Evaluating Expressions
15m

Translating Phrases to Expressions
16m

Simplifying Expressions
44m

2. Linear Equations and Inequalities2h 56m

Solving Linear Equations
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Linear Inequalities in One Variable
46m

Set Operations and Compound Inequalities
42m

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Introduction to Problem Solving
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Percent Problem Solving
36m

4. Graphs and Functions2h 48m

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25m

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13m

Introduction to Relations and Functions
25m

Function Notation
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5. Systems of Linear Equations1h 12m

Solving Systems of Linear Equations by Graphing
29m

Solving Systems of Linear Equations by Substitution
15m

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6. Exponents, Polynomials, and Polynomial Functions1h 27m

The Product Rule
9m

The Quotient Rule
10m

Intro to the Power Rules
17m

Simplifying Exponential Expressions Using All Exponent Rules
6m

Intro to Polynomials
5m

Multiplying Polynomials
38m

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Factoring by Greatest Common Factor & Grouping
26m

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

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

Quadratic Equations & Applications
14m

8. Rational Expressions and Functions2h 21m

Simplifying Rational Expressions
33m

Least Common Denominators
32m

Adding and Subtracting Rational Expressions with Different Denominators
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44m

9. Roots, Radicals, and Complex Numbers2h 33m

Introduction to Radical Expressions
11m

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27m

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19m

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23m

Introduction to Complex Numbers
18m

Multiplying and Dividing Complex Numbers
51m

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The Square Root Property
25m

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26m

The Quadratic Formula
31m

11. Inverse, Exponential, & Logarithmic Functions1h 5m

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Introduction to Logarithmic Functions
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6. Exponents, Polynomials, and Polynomial Functions

The Product Rule

Intermediate Algebra

6. Exponents, Polynomials, and Polynomial Functions

The Product Rule

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Multiple Choice

Simplify each expression.
$(- 5 a^{2}) (3 a^{8})$

$- 2 a^{10}$

$- 15 a^{6}$

$- 5 a^{10}$

$- 15 a^{10}$

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Verified step by step guidance

Identify the expression to simplify: $(-5a^{2})(3a^{8})$.

Multiply the numerical coefficients: $-5 \times 3$.

Apply the product rule for exponents on the variable $a$: when multiplying like bases, add the exponents, so $a^{2} \times a^{8} = a^{2+8}$.

Combine the results from the previous steps to write the simplified expression as the product of the new coefficient and the variable with the summed exponent.

Write the final simplified expression in the form $-15a^{10}$ (without calculating the numeric value explicitly here).

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Simplify each expression.(−5a2)(3a8)(-5a^2)(3a^8)

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Simplify each expression.
$(- 5 a^{2}) (3 a^{8})$