Express 64, start superscript, start fraction, 2, divided by, 3, end fraction, end superscript64
3
2
​

in simplest radical form.

To express \( 64^{\frac{2}{3}} \) in its simplest radical form, follow these steps:

1. **Understand the expression:** 
   \[
   64^{\frac{2}{3}} = \left(64^{\frac{1}{3}}\right)^2
   \]
   The exponent \( \frac{2}{3} \) means that you first take the cube root of 64, and then square the result.

2. **Calculate the cube root of 64:**
   \[
   64^{\frac{1}{3}} = \sqrt[3]{64} = 4
   \]
   Since \( 4^3 = 64 \), the cube root of 64 is 4.

3. **Square the result:**
   \[
   \left(4\right)^2 = 16
   \]

So, the expression \( 64^{\frac{2}{3}} \) in its simplest radical form is \( \boxed{16} \).

Would you like more details on this, or do you have any questions?

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Here are 5 related questions:
1. How do you simplify \( 81^{\frac{3}{4}} \) in radical form?
2. What is the simplest radical form of \( 32^{\frac{4}{5}} \)?
3. How do you express \( 125^{\frac{2}{3}} \) in radical form?
4. What is the value of \( 100^{\frac{3}{2}} \)?
5. How do you simplify \( 216^{\frac{1}{3}} \)?

**Tip:** When dealing with fractional exponents, the numerator is the power and the denominator is the root.

Learn how to express 64^(2/3) in its simplest radical form with a step-by-step solution. Understand the concept of fractional exponents and radical forms. Suitable for Grades 9-12.

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