The image presents four options related to the equation involving the fourth root of 16. Let's analyze each option to determine the correct equality.

The fourth root of 16 is defined as the number that, when raised to the power of 4, equals 16:

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

Now, let's evaluate the options:

• Option a: $-\sqrt[4]{16} = -2$

  This is correct because $\sqrt[4]{16} = 2$, so $-\sqrt[4]{16} = -2$.

• Option b: $\sqrt[4]{16} = \pm 2$

  This is incorrect because the fourth root of a positive number (16) should be only positive 2, not $\pm 2$.

• Option c: $\sqrt[4]{-16} = 2$

  This is incorrect because the fourth root of a negative number does not result in a real number.

• Option d: $\sqrt[4]{16} = -2$

  This is incorrect because $\sqrt[4]{16} = 2$, not $-2$.

Correct answer: Option a is the correct equation.

Do you have any questions or want further details?

Here are some related questions:

1. What is the principal square root of a positive number?
2. How is the fourth root of a number calculated?
3. Why can we not take the fourth root of a negative number in real numbers?
4. What is the difference between an even root and an odd root of negative numbers?
5. Can roots of even degree have negative solutions in real numbers?

Tip: When calculating even roots (like square roots or fourth roots), the result is always non-negative in real numbers unless explicitly negated!