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Chapter 5: Problem 32

Multiply the monomials. $$\left(-\frac{1}{3} a^{4}\right)\left(-\frac{1}{2} a^{2}\right)$$

Short Answer

Expert verified
\(\frac{1}{6}a^{6}\)

Step by step solution

01

Identify the Coefficients and Variables

The coefficients in the monomials are \(-\frac{1}{3}\) and \(-\frac{1}{2}\). The variables in the monomials are \(a^{4}\) and \(a^{2}\).
02

Multiply the Coefficients

When multiplying monomials, the coefficients (numbers) are multiplied together as well. Multiply \(-\frac{1}{3}\) and \(-\frac{1}{2}\) to get a result of \(\frac{1}{6}\). It is important to remember that a negative times a negative equals a positive.
03

Apply the Laws of Exponents

When multiplying terms with the same base, you keep the base and add the exponents. Here, keep the base \(a\) and add the exponents \(4 + 2\) to get \(a^{6}\).
04

Combine the Results

Combine the results from steps 2 and 3. Multiply coefficient, derived from step 2, and the variable \(a^{6}\) derived from step 3, to get the final result \(\frac{1}{6}a^{6}\).

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Most popular questions from this chapter

In Exercises \(79-82,\) simplify each expression. $$\left(\frac{18 x^{2} y^{4}}{9 x y^{2}}\right)-\left(\frac{15 x^{5} y^{6}}{5 x^{4} y^{4}}\right)$$

Explain how to divide a polynomial that is not a monomial by a monomial. Give an example.

Explain how to multiply polynomials when neither is a monomial. Give an example.

Explain how to simplify an expression that involves a quotient raised to a power. Provide an example with your explanation.

Perform the indicated operations. $$(y+5)^{2}-(y-4)^{2}$$
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