Chapter 4.5, Problem 53E

To determine

To simplify the following expression $\frac{28c^{10}{d}^{13}}{24c^6{d}^8}$

Answer to Problem 53E

  $\frac{7c^4{d}^5}{6}$

Explanation of Solution

Given information:Simplify: $\frac{28c^{10}{d}^{13}}{24c^6{d}^8}$

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.

Given, $\frac{28c^{10}{d}^{13}}{24c^6{d}^8}$

  $=\frac{2^2\times 7\times c^{10}\times d^{13}}{2^3\times 3\times c^6\times d^8}$ Here, it can be written as28 as $2^2\times 7$ and 24 as $2^3\times 3$

  $=\frac{7\times c^{10-6}\times d^{13-8}}{2^{3-1}\times 3}$ Here, the exponents of the bases ‘c’, ‘d’, and 2 are adjusted

  $=\frac{7c^4{d}^5}{6}$ This is the simplified expression.