Chapter 4.5, Problem 51E

To determine

To simplify the following expression $\frac{63m^5{n}^6}{27mn}$

Answer to Problem 51E

  $\frac{7m^4{n}^5}{3}$

Explanation of Solution

Given information:

  $\frac{63m^5{n}^6}{27mn}$

This answer shall be derived using the product of powers rule, wherein the exponents of a common base can be added during multiplication and subtracted during division.

Calculation:

Given, $\frac{63m^5{n}^6}{27mn}$

  $=\frac{3^2\times 7\times m^5\times n^6}{3^3\times m\times n}$ Here, it can be written as 63 as $3^2*7$ and 27 as $3^3$

  $=\frac{7\times m^{5-1}\times n^{6-1}}{3^{3-2}}$ Here, the exponents of the bases ‘m’, ‘n’, and 3 are added.

  $=\frac{7m^4{n}^5}{3}$ This is the simplified expression.