Problem 15 Multiply. $$ \left(-0.1 x^{6... [FREE SOLUTION]

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Chapter 5: Problem 15

Multiply. $$ \left(-0.1 x^{6}\right)\left(0.2 x^{4}\right) $$

Short Answer

Expert verified

-0.02x^{10}

Step by step solution

Multiply the coefficients

Multiply $-0.1$ by $0.2$. $-0.1 \times 0.2 = -0.02$.

Add the exponents of the base

Since both terms have $x$ as the base, add the exponents. $6 + 4 = 10$.

Combine the results

Combine the multiplied coefficients and the new exponent. The result is $-0.02 x^{10}$.

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Key Concepts

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

coefficients multiplication

When you multiply polynomials, you first look at the numbers in front of the variables, known as coefficients. In our example, we have \-0.1\thinspace and \-0.2\thinspace. We need to multiply these two numbers together:

-0.1 $\times$ 0.2 equals -0.02.

This multiplication can be done just like any other multiplication of decimal numbers. Ignore the negative signs and multiply as usual, then add the negative sign back if necessary.

If you're not confident with multiplying decimals, remember to count the total number of decimal places in the numbers you are multiplying. This will help you place the decimal point correctly in your answer.

exponent addition

Next, let's move to the variables. When multiplying terms with the same base, we add their exponents. Here, both terms have the base $x$. So, we will add the exponents from the $x\^{6}$ and $x\^{4}$:

6 + 4 equals 10.

This means, the new exponent for $x$ in our answer will be 10. Remember that this rule only applies when the bases of the variables are the same.

combining terms

Finally, we combine our results. We have already found the new coefficient and the new exponent. Our coefficient is \-0.02\thinspace and our new exponent is 10. When putting them together, our expression looks like this:

-0.02 $x\^{10}$

So, this is our final answer.

Understanding how to combine all these parts is crucial for polynomial multiplication. By breaking it down into smaller steps like this, we can make the problem more manageable.

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91影视

Multiply. $$ \left(-0.1 x^{6}\right)\left(0.2 x^{4}\right) $$

Short Answer

Step by step solution

Multiply the coefficients

Add the exponents of the base

Combine the results

Key Concepts

coefficients multiplication

exponent addition

combining terms

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