Chapter 6, Problem 1CT

To determine

To Evaluate: The expression $-\sqrt[4]{16}$

Answer to Problem 1CT

The value of $-\sqrt[4]{16}=-2$

Explanation of Solution

Given information:

The expression $-\sqrt[4]{16}$

Concept and Formula Used:

Rule of exponent and addition and subtraction.

  $a^n=a\times a\times a\times \mathrm{..................}n\text{ times,}\sqrt[n]{a}={\left(a\right)}^{\frac{1}{n}}\&{\left(a^m\right)}^n=a^{mn}$

Calculation:

The given expression is

  $\begin{array}{l}-\sqrt[4]{16}\\ \text{Factor 16}\\ -\sqrt[4]{16}=-\sqrt[4]{2\times 2\times 2\times 2}\\ \text{Using }\sqrt[n]{a}={\left(a\right)}^{\frac{1}{n}}\\ -\sqrt[4]{16}=-{\left(2^4\right)}^{\frac{1}{4}}\\ \text{Using }{\left(a^m\right)}^n=a^{mn}\\ -\sqrt[4]{16}=-{\left(2\right)}^{4\times \frac{1}{4}}\\ -\sqrt[4]{16}=-{\left(2\right)}^1\\ -\sqrt[4]{16}=-2\end{array}$

Conclusion:

The value of $-\sqrt[4]{16}=-2$