Chapter 6.1, Problem 1E

Solution

To simplify: The expression $\left(2a^3\right)\left(5a^4\right)$ .

  $10a^7$

Given information:

The expression $\left(2a^3\right)\left(5a^4\right)$ .

Concept used:

Exponent rules: $a^m{b}^m={\left(ab\right)}^m$ , $a^b\cdot a^c=a^{b+c}$ , ${\left(a^b\right)}^c=a^{bc}$ , $a^b\cdot a^c=a^{b+c}$ .

Calculation:

Simplify the expression as follows:

  $\begin{array}{c}\left(2a^3\right)\left(5a^4\right)=2\cdot 5a^{3+4}\\ =2\cdot 5a^7\\ =10a^7\end{array}$

Conclusion:

The simplified expression is $10a^7$ .