Chapter 4.5, Problem 49E

To determine

To simplify the following expression $4ab(0.5a^2{b}^3)$

Answer to Problem 49E

  $2a^3{b}^4$

Explanation of Solution

Given information:

  $4ab(0.5a^2{b}^3)$

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, $4ab(0.5a^2{b}^3)$

  $=2^2\times a\times b\times \frac{1}{2}\times a^2\times b^3$ Here, it’s written 0.5 as $\frac{1}{2}$ . This could be further written as $2^{-1}$

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

  $=2a^3{b}^4$ This is the simplified expression.