Chapter 4.5, Problem 55E

To determine

To simplify the following expression $\frac{3a·4a^4}{28a^2}$

Answer to Problem 55E

  $\frac{3a^3}{7}$

Explanation of Solution

Given information:

  $\frac{3a·4a^4}{28a^2}$

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, $\frac{3a·4a^4}{28a^2}$

  $=\frac{3\times a\times 2^2\times a^4}{2^2\times 7\times a^2}$ Here, it’s written as 4 as $2^2$ and 28 as $2^2\times 7$

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

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