Chapter 7.2, Problem 52PPS

To determine

To simplify the given expression.

Answer to Problem 52PPS

  $\frac{{\left(5p{r}^{-2}\right)}^{-2}}{{\left(3p^{-1}r\right)}^3}=\frac{pr}{675}$

Explanation of Solution

Given:

  $\frac{{\left(5p{r}^{-2}\right)}^{-2}}{{\left(3p^{-1}r\right)}^3}$

Calculation:

  $\frac{{\left(5p{r}^{-2}\right)}^{-2}}{{\left(3p^{-1}r\right)}^3}=\frac{{\left(5\right)}^{-2}{\left(p\right)}^{-2}{\left(r^{-2}\right)}^{-2}}{{\left(3\right)}^3{\left(p^{-1}\right)}^3{\left(r\right)}^3}$

  $=\frac{p^{-2}{r}^4}{{\left(5\right)}^2\times {\left(3\right)}^3{p}^{-3}{r}^3}$

  $=\frac{p^{-2}\times p^3\times r^3\times r}{25\times 27r^3}$

  $=\frac{p^{-2+3}\times r}{675}$

  $=\frac{pr}{675}$