Chapter 4.7, Problem 6MRE

To determine

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

Answer to Problem 6MRE

  $-27x^9$

Explanation of Solution

Given information:

The expression, ${\left(-3x^3\right)}^3$

Concept used:

Exponent property: ${\left(a\cdot b\right)}^n=a^n\cdot b^n$

Exponent property: ${\left(a^n\right)}^m=a^{n\cdot m}$

Calculation:

In order to simplify the given expression ${\left(-3x^3\right)}^3$ , use the exponent property and simplify further as shown below

  $\begin{array}{c}{\left(-3x^3\right)}^3={\left(-3\right)}^3\cdot {\left(x^3\right)}^3\\ =\left(-27\right)\cdot \left(x^{3\cdot 3}\right)\\ =-27\cdot x^9\\ =-27x^9\end{array}$

Thus, the given expression simplifies to $-27x^9$ .