Chapter 4, Problem 7CR

To determine

To simplify the expression ${\left(-3x^2{y}^4\right)}^3$ .

Answer to Problem 7CR

  $d.-27x^6{y}^{12}$

Explanation of Solution

Given information:

The expression ${\left(-3x^2{y}^4\right)}^3$

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, use the product to power property and power property of exponents and simplify further as shown below,

  $\begin{array}{c}{\left(-3x^2{y}^4\right)}^3={\left(-3\right)}^3{\left(x^2\right)}^3{\left(y^4\right)}^3\\ =\left(-27\right)\left(x^{2\cdot 3}\right)\left(y^{4\cdot 3}\right)\\ =\left(-27\right)\left(x^6\right)\left(y^{12}\right)\\ =-27x^6{y}^{12}\end{array}$

Thus, the given expression simplifies to $-27x^6{y}^{12}$ .