Chapter 4.3, Problem 7MRE

To determine

To simplify: The given expression.

Answer to Problem 7MRE

  ${\left(-u^2\right)}^4{\left(-u\right)}^3$ is simplified as $u^{11}$ .

Explanation of Solution

Given:

The following expression:

  ${\left(-u^2\right)}^4{\left(-u\right)}^3$

Formula used:

The first law of exponents:

  $a^m\cdot a^n=a^{m+n}$

The third law of exponents:

  ${\left(a^m\right)}^n=a^{mn}$

Calculation:

The given expression can be simplified as:

  $\begin{array}{l}{\left(-u^2\right)}^4{\left(-u\right)}^3[\text{Given]}\\ =u^8\cdot u^3[\text{Third law of exponents]}\\ =u^{8+3}[\text{First law of exponents]}\\ =u^{11}[\text{Simplify]}\end{array}$