Chapter 9, Problem 36SGR

To determine

To calculate: To find the product or quotient and express using exponents

Answer to Problem 36SGR

Product is $-30a^7$

Explanation of Solution

Given information: Expression is $\left(5a^3\right)\left(-6a^4\right)$

Formula Used:

Exponential identities are

  $x^a{x}^b=x^{a+b}$

  $x^a{y}^a={\left(xy\right)}^a$

  ${\left(x^a\right)}^b={\left(x\right)}^{ab}$

  $\frac{x^a}{x^b}={\left(x\right)}^{a-b}$

Calculation:

Expression is given as

  $\left(5a^3\right)\left(-6a^4\right)$

On solving the above expression using the exponential identity $x^a{x}^b=x^{a+b}$

  $\begin{array}{l}\left(5a^3\right)\left(-6a^4\right)=\left(5\times -6\right)\left(a^3{a}^4\right)\\ \left(5a^3\right)\left(-6a^4\right)=\left(-30\right)\left(a^{3+4}\right)\\ \left(5a^3\right)\left(-6a^4\right)=-30a^7\end{array}$

Conclusion:

Hence, product is $-30a^7$