https://file.aiquickdraw.com/mathbot/file/172917624766659h31tnf.jpg

The expression presented in the image is:

\[
216^{\frac{1}{3}} - (16)^{\frac{1}{4}} + (125)^{\frac{2}{3}}
\]

Let's break down and simplify this step by step:

1. **\( 216^{\frac{1}{3}} \):** This represents the cube root of 216. Since \( 216 = 6^3 \), the cube root of 216 is 6.

   \[
   216^{\frac{1}{3}} = 6
   \]

2. **\( 16^{\frac{1}{4}} \):** This represents the fourth root of 16. Since \( 16 = 2^4 \), the fourth root of 16 is 2.

   \[
   (16)^{\frac{1}{4}} = 2
   \]

3. **\( 125^{\frac{2}{3}} \):** This represents the cube root of 125, squared. First, \( 125 = 5^3 \), so the cube root of 125 is 5. Then we square the result:

   \[
   (125)^{\frac{1}{3}} = 5 \quad \text{and} \quad (5)^2 = 25
   \]

Now, we combine all the results:

\[
6 - 2 + 25 = 29
\]

Thus, the value of the expression is:

\[
\boxed{29}
\]

Let me know if you would like more details on any step, or if you have any questions!

Here are some related questions to expand on this topic:
1. What is the general rule for simplifying fractional exponents?
2. How would the result change if one of the numbers was negative?
3. Can you find the cube root of other numbers using a similar method?
4. What happens if you need to calculate higher-order roots, like a fifth or sixth root?
5. Can this expression be represented in a logarithmic form?

**Tip:** When working with fractional exponents, always remember that the denominator represents the root and the numerator represents the power to which the root is raised!

Nilai dari 216^(1/3) - (16)^(1/4) + (125)^(2/3) adalah...

Learn how to simplify an expression with fractional exponents, including cube roots, fourth roots, and powers of rational numbers. This step-by-step guide covers the problem 216^(1/3) - (16)^(1/4) + (125)^(2/3), with solutions based on the laws of exponents. Suitable for students in Grades 10-12.

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