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Chapter 5: Problem 33

Multiply the monomials. $$\left(2 x^{2}\right)(-3 x)\left(8 x^{4}\right)$$

Short Answer

Expert verified
The result is -48\(x^{7}\).

Step by step solution

01

Multiply the coefficients

First, multiply the coefficients of the monomials, which are the numbers in front of the \(x\) variables. So \(2 * -3 * 8 = -48\)
02

Apply the rule of exponents

Next, because the base for all the exponents is \(x\), the exponents are added together. The rule is: \(a^{m} * a^{n} = a^{m+n}\). Therefore, for our problem, \(x^{2} * x * x^{4} = x^{2+1+4} = x^{7}\)
03

Write the final answer

Finally, combine the result from step 1 and step 2 to write the final answer. The coefficient is -48 and the variable part is \(x^{7}\). So the product of the monomials is -48\(x^{7}\)

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Most popular questions from this chapter

In Exercises \(79-82,\) simplify each expression. $$\frac{6 x^{3}(3 x-1)+5 x^{2}(6 x-3)}{3 x^{2}}$$

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