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Chapter 5: Problem 31

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

Short Answer

Expert verified
The solution to the multiplication problem is \(\frac{1}{8}a^{5}\).

Step by step solution

01

Multiply the Numerical Coefficients

First, multiply the numerical coefficients of each monomial together. In this case, \(-\frac{1}{2}\) and \(-\frac{1}{4}\). The product of two negative numbers is a positive number, so the numerical coefficient of the product is \(\frac{1}{8}\).
02

Combine the Literal Coefficients

The next step is to combine the powers of the literal coefficient 'a' using the law of exponents: when multiplying two powers of the same base, add the exponents together. Therefore, \(a^{3}\) and \(a^{2}\) combine to become \(a^{5}\).
03

Formation of Solution

Finally, combine the numerical and literal coefficients to form the overall solution of the problem: \(\frac{1}{8}a^{5}\).

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Most popular questions from this chapter

Use a vertical format to find each product. $$\begin{array}{r}7 x^{3}-5 x^{2}+6 x \\\3 x^{2}-4 x \\\\\hline\end{array}$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$4^{-2}<4^{-3}$$

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

Simplify each exponential expression. Assume that variables represent nonzero real numbers. $$\frac{\left(2^{1} x^{3} y^{-1}\right)^{-2}\left(2 x^{6} y^{4}\right)^{-2}\left(9 x^{3} y^{3}\right)^{0}}{\left(2 x^{4} y^{6}\right)^{2}}$$

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