Chapter 4.5, Problem 50E

To determine

To simplify the following expression $\frac{14a^3{b}^4}{4ab}$

Answer to Problem 50E

  $\frac{7a^2{b}^3}{2}$

Explanation of Solution

Given information:

  $\frac{14a^3{b}^4}{4ab}$

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, $\frac{14a^3{b}^4}{4ab}$

  $=\frac{2\times 7\times a^3\times b^4}{2^2\times a\times b}$ Here, it’swritten14 as 2*7 and 4 as $2^2$

  $=\frac{7\times a^{3-1}\times b^{4-1}}{2^{2-1}}$ Here, the exponents of the bases ‘a’, ‘b’, and 2 are added.

  $=\frac{7a^2{b}^3}{2}$ This is the simplified expression.