cube root of 16 simplified
Understand the Problem
The question is asking for the simplified form of the cube root of 16. This involves finding a number that, when multiplied by itself three times, equals 16.
Answer
The simplified form of the cube root of 16 is $2 \sqrt[3]{2}$.
Answer for screen readers
The simplified form of the cube root of 16 is $2 \sqrt[3]{2}$.
Steps to Solve

Express the number as a power To simplify the cube root of 16, we can express 16 as a power of 2. Since $16 = 2^4$, we can rewrite the cube root as follows: $$ \sqrt[3]{16} = \sqrt[3]{2^4} $$

Use the properties of exponents When taking the cube root of a power, we can use the property of exponents which states that $\sqrt[n]{a^m} = a^{\frac{m}{n}}$. Therefore, we can write the expression as: $$ \sqrt[3]{2^4} = 2^{\frac{4}{3}} $$

Rewriting the exponent The exponent $\frac{4}{3}$ can be expressed as a mixed number. This means we can write: $$ 2^{\frac{4}{3}} = 2^{1 + \frac{1}{3}} = 2^1 \cdot 2^{\frac{1}{3}} $$

Calculate the values Now we can substitute back to obtain the simplified expression. Calculating $2^1$ gives us 2: $$ 2^1 = 2 $$ Thus, the expression simplifies to: $$ 2 \cdot \sqrt[3]{2} $$
The simplified form of the cube root of 16 is $2 \sqrt[3]{2}$.
More Information
The cube root function finds the number that, when cubed (multiplied by itself two more times), gives the original number. In this case, expressing 16 as $2^4$ made it easier to simplify the cube root.
Tips
 Confusing the cube root with the square root. Remember, we're dealing with the cube root here.
 Not expressing 16 in terms of its prime factors, which simplifies the computation of roots.