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Chapter 5: Problem 28

Find each product. $$\left(10 x^{2} y\right)(5 x y)$$

Short Answer

Expert verified
The product of \(10x^{2}y\) and \(5xy\) is \(50x^{3}y^{2}\).

Step by step solution

01

Apply Coefficient Multiplication

Multiply the numerical coefficients, which are 10 and 5, first. This results in a coefficient of 50 for the product.
02

Apply Variable Multiplication

Next, multiply the same base variables. When multiplying variables with exponents, add the exponents. This gives \(x^{2+1}\) or \(x^{3}\) and \(y^{1+1}\) or \(y^{2}\).
03

Combine Results

Combine the products of the coefficients and variables to get the final answer. Therefore, the product is \(50x^{3}y^{2}\).

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Most popular questions from this chapter

In Exercises \(105-106,\) find the missing coefficients and exponents designated by question marks. $$\frac{3 x^{14}-6 x^{12}-7 x^{7}}{2 x^{7}}=-x^{7}+2 x^{5}+3$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\left(4 \times 10^{3}\right)+\left(3 \times 10^{2}\right)=4.3 \times 10^{3}$$

Use a vertical format to find each product. $$\begin{array}{l}x^{2}+7 x-3 \\\x^{2}-x-1 \\\\\hline\end{array}$$

Explain the power rule for exponents. Use \(\left(3^{2}\right)^{4}\) in your explanation.

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