Chapter 4.3, Problem 15WE

To determine

To Simplify: The expression $\left(5a^2{b}^{3}c\right)\left(2a{b}^4{c}^2\right)$

Answer to Problem 15WE

The required answer is $10a^3{b}^7{c}^3$ .

Explanation of Solution

Given information:

The expression $\left(5a^2{b}^{3}c\right)\left(2a{b}^4{c}^2\right)$

Concept Used:

Rule of exponents for product of powers states that to multiply two powers with same base, the exponents are added.

For example $a^m\cdot a^n=a^{m+n}$

Commutative property of multiplication states that the product of any numbers remains the same irrespective of the order in which we multiply.

For example:

  $2\cdot 5=5\cdot 2=10$

Associative property of multiplication states that the product of the any numbers remains the same regardless of the grouping of factors.

For example:

  $2\left(5\cdot 3\right)=\left(2\cdot 5\right)\cdot 3=30$

Calculation:

  $\left(5a^2{b}^{3}c\right)\left(2a{b}^4{c}^2\right)$

Commutative and Associative property of multiplication.

  $=\left(5\cdot 2\right)\left(a^2\cdot a\right)\left(b^3\cdot b^4\right)\left(c\cdot c^2\right)$

Using rule of exponents for product of powers

  $\begin{array}{l}=10a^{2+1}{b}^{3+4}{c}^{1+2}\\ =10a^3{b}^7{c}^3\end{array}$