Chapter 12.5, Problem 8MRE

To determine

Write the expression ${\left(-5a^{3}b\right)}^2{\left(2a^{2}b\right)}^3$ in simplest form without negative exponents.

Answer to Problem 8MRE

The simplest form of expression is $200a^{12}{b}^5$ .

Explanation of Solution

Given information: The given expression is,

  ${\left(-5a^{3}b\right)}^2{\left(2a^{2}b\right)}^3\mathrm{....}\left(1\right)$

Calculation: Simplify (1),

  $\begin{array}{c}{\left(-5a^{3}b\right)}^2{\left(2a^{2}b\right)}^3=\left({\left(-5\right)}^2{\left(a^3\right)}^2{\left(b\right)}^2\right)\left({\left(2\right)}^3{\left(a^2\right)}^3{\left(b\right)}^3\right)\\ =\left(25a^6{b}^2\right)\left(8a^6{b}^3\right)\\ =200\left\{{\left(a\right)}^{6+6}{\left(b\right)}^{2+3}\right\}\\ =200a^{12}{b}^5\end{array}$

Hence the simplest form of expression is $200a^{12}{b}^5$ .