Chapter 5, Problem 1RP

To determine

The simplified form of expression $\left(-6a^2\right)\left(3a^5\right)$ .

Answer to Problem 1RP

Solution: The simplified form of expression $\left(-6a^2\right)\left(3a^5\right)$ is $-18a^7$ .

Explanation of Solution

Given: The given expression is $\left(-6a^2\right)\left(3a^5\right)$ .

Calculation:

In order to multiply two exponential expressions that have same base, keep the base and add the exponent.

  $x^a\cdot x^b=x^{a+b}$

Simplify the expression $\left(-6a^2\right)\left(3a^5\right)$ .

  $\begin{array}{c}\left(-6a^2\right)\left(3a^5\right)\\ =-6\times a^2\times 3\times a^5\\ =-6\times 3\times a^2\times a^5\left(\text{Multiply}\text{the}\text{numerical}\text{coefficients}\right)\\ =-18\times a^{2+5}\left(\text{Use}\text{the}\text{product}\text{rule}\left(x^a\cdot x^b=x^{a+b}\right)\right)\\ =-18a^7\end{array}$

The simplified form of expression $\left(-6a^2\right)\left(3a^5\right)$ is $-18a^7$ .

Conclusion:

Therefore, the simplified form of expression $\left(-6a^2\right)\left(3a^5\right)$ is $-18a^7$ .