Chapter 4, Problem 7CT

To determine

To simplify the expression $4y^3\left(-3xy\right)$ .

Answer to Problem 7CT

  $-12x{y}^4$

Explanation of Solution

Given information:

The expression $4y^3\left(-3xy\right)$

Concept used:

Exponent properties: If a , b are real numbers and m , n are whole numbers, then

• Product Property: $a^m\cdot a^n=a^{m+n}$
• Power Property: ${\left(a^m\right)}^n=a^{m\cdot n}$
• Product to a Power Property: ${\left(ab\right)}^m=a^m{b}^m$

Calculation:

In order to simplify the given expression $4y^3\left(-3xy\right)$ , multiply the numbers and variables together and simplify further using the product to power property of exponents as shown below,

  $\begin{array}{c}4y^3\left(-3xy\right)=\left(4\cdot \left(-3\right)\right)\left(x\right)\left(y^3\cdot y\right)\\ =\left(-12\right)\left(x\right)\left(y^{3+1}\right)\\ =\left(-12\right)\left(x\right)\left(y^4\right)\\ =-12x{y}^4\end{array}$

Thus, the given expression simplifies to$-12x{y}^4$ .