Question

use radical notation to rewrite the expression. simplify, if possible.

\\ -16^{1/4} \\

select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. \\( -16^{1/4} = \\)
b. the root is not a real number.

Explanation:

⚡ Using what you learned: Integer and Rational Exponents

Step 1: Apply order of operations

The negative sign is outside the base because there are no parentheses grouping them together.

$$ -16^{1/4} = -(16^{1/4}) $$

Step 2: Rewrite in radical notation

A rational exponent of \( \frac{1}{n} \) represents the \( n \)-th root.

$$ -(16^{1/4}) = -\sqrt[4]{16} $$

Step 3: Simplify the root

Find the number that, when multiplied by itself 4 times, equals 16.

$$ 2 \times 2 \times 2 \times 2 = 16 \implies \sqrt[4]{16} = 2 $$

Apply the negative sign outside:

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

Answer:

A. \( -16^{1/4} = -2 \)