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Chapter 5: Problem 29

Multiply the monomials. $$\left(-5 y^{4}\right)\left(3 y^{3}\right)$$

Short Answer

Expert verified
The solution to the multiplication of the monomials \(-5y^{4}\) and \(3y^{3}\) is \(-15y^{7}\).

Step by step solution

01

Multiply the Coefficients

First, multiply the numerical coefficients of the monomials. In this case, it is \( -5 \) and \( 3 \), which gives \( -5 \times 3 = -15 \).
02

Multiply the Variables with Exponents

Next, multiply the variables with exponents. We have \( y^{4} \) and \( y^{3} \). When multiplying terms with the same base, we add the exponents. Therefore, \( y^{4} \times y^{3} = y^{4+3} = y^{7} \).
03

Combine the Results

Finally, combine the results from the first two steps. Bring together the product of the coefficients and the product of the variables to obtain the final solution. We get \( -15 \times y^{7} = -15y^{7} \).

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Most popular questions from this chapter

Explain the product rule for exponents. Use \(2^{3} \cdot 2^{5}\) in your explanation.

Will help you prepare for the material covered in the next section. In each exercise, find the indicated products. Then, if possible, state a fast method for finding these products. (You may already be familiar with some of these methods from a high school algebra course.) a. \((x+3)^{2}\) b. \((x+5)^{2}\)

Use a vertical format to find each product. $$\begin{array}{r} 9 y^{3}-7 y^{2}+5 y \\ 3 y^{2}+5 y \\ \hline \end{array}$$

Explain how to find any nonzero number to the 0 power.

Perform the indicated operations. $$(x+5)(x-6)-(x+2)(x-9)$$
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