Problem 6 Find each product. $$ -3 m^{... [FREE SOLUTION]

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Beginning Algebra

Margaret L. Lial, John Hornsby

$Math Studyset 91影视 Explanations$ Math

11 Edition

Chapter 5: Problem 6

Find each product. $$ -3 m^{6}\left(-5 m^{4}\right) $$

Short Answer

Expert verified

15m^{10}

Step by step solution

Identify the Coefficients

The first step is to identify the numerical coefficients in the expression. Here, the coefficients are -3 (from -3 m^{6}) and -5 (from -5 m^{4}).

Multiply the Coefficients

Multiply the numerical coefficients together: $-3 \times -5 = 15$.

Identify and Add the Exponents

Identify the exponents of the variable m. In -3 m^{6} , the exponent is 6 . In -5 m^{4} , the exponent is 4. When multiplying like bases, add the exponents: 6 + 4 = 10.

Combine the Results

Combine the new coefficient and the new exponent to get the final product: 15m^{10} .

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Multiplying Exponents

Multiplying exponents is a key concept in algebra. When you multiply similar bases, you add their exponents. For example, if you have two terms with the base $m$, like $m^6$ and $m^4$, you add the exponents:

$m^6 \times m^4 = m^{6+4} = m^{10}$

This rule makes it easier to simplify expressions involving powers. Always ensure the bases are the same before adding exponents.

Coefficients

Coefficients are the numerical parts in an algebraic term. In the expression $-3m^6$,

-3 is the coefficient, and $m^6$ is the variable raised to an exponent. In another term like $-5m^4$, -5 is the coefficient.

Here鈥檚 an example: To find the product of $-3m^6$ and $-5m^4$, first multiply the coefficients ($-3$ and $-5$). When multiplying these coefficients,

remember the rule: a negative times a negative gives a positive. So, $-3 \times -5 = 15$.

This step effectively simplifies the numerical part of your expression.

Step-by-Step Algebra

To solve algebra problems effectively, follow a step-by-step approach. Let's break down the exercise involving $-3m^6\left(-5m^4\right)$:
Step 1: Identify the Coefficients

Look for the numbers in front of the variables. Here, the coefficients are $-3$ and $-5$.

Step 2: Multiply the Coefficients

Multiply these numbers together: $-3 \times -5 = 15$.

Step 3: Identify and Add the Exponents

For the variable part, notice the exponents: $m^6$ and $m^4$.
Add the exponents because the bases are the same: $6 + 4 = 10$.
$m^6 \times m^4 = m^{10}$.

Step 4: Combine the Results

Join the new coefficient and exponent to form the simplified term: $15m^{10}$.

Following these steps ensures accuracy and clarity in solving algebraic expressions.

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91影视

Find each product. $$ -3 m^{6}\left(-5 m^{4}\right) $$

Short Answer

Step by step solution

Identify the Coefficients

Multiply the Coefficients

Identify and Add the Exponents

Combine the Results

Key Concepts

Multiplying Exponents

Coefficients

Step-by-Step Algebra

One App. One Place for Learning.

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