Chapter 4.5, Problem 54E

To determine

To simplify the following expression $\frac{2x^6·4x^3}{24x^5}$

Answer to Problem 54E

  $\frac{x^4}{3}$

Explanation of Solution

Given information:Simplify $\frac{2x^6·4x^3}{24x^5}$

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, $\frac{2x^6·4x^3}{24x^5}$

  $=\frac{2^1\times x^6\times 2^2\times x^3}{2^3\times 3\times x^5}$ Here, it’s written as 4 as $2^2$ and 24 as $2^3\times 3$

  $=\frac{2^{1+2-3}\times x^{6+3-5}}{3}$ Here, the exponents of the bases ‘x’, and 2 are adjusted.

  $=\frac{x^4}{3}$ This is the simplified expression.