https://file.aiquickdraw.com/mathbot/file/1725923226344pg66jw9k.jpg

The problem requires converting the expression from radical form to rational exponent form.

### Given:
- Radical Form: \( \sqrt[4]{256^3} = 64 \)

### Conversion to Rational Exponent Form:

The radical expression \( \sqrt[4]{256^3} \) can be rewritten using rational exponents. The general conversion rule is:

\[
\sqrt[n]{a^m} = a^{\frac{m}{n}}
\]

In this case:
- \( a = 256 \)
- \( m = 3 \)
- \( n = 4 \)

Thus, the expression becomes:

\[
256^{\frac{3}{4}}
\]

### Rational Exponent Form:
\[
256^{\frac{3}{4}} = 64
\]

### Answer:
The missing form in "Rational Exponent Form" is \( 256^{\frac{3}{4}} \).

Would you like more details or have any questions? Here are some related questions to consider:

1. How do you convert between radical form and rational exponent form in general?
2. What are the properties of exponents that are useful in these conversions?
3. Can you provide another example involving a different root, such as a cube root?
4. How would you simplify \( 256^{\frac{1}{4}} \) step-by-step?
5. What are some common mistakes to avoid when converting between radical and rational exponent forms?

**Tip:** When converting between radical and exponent forms, always remember that the root becomes the denominator of the exponent, and the power becomes the numerator.

Fill in the missing form. Convert the given radical form to rational exponent form: \( \sqrt[4]{256^3} = 64 \).

Understand how to convert from radical form to rational exponent form with this example: \( \sqrt[4]{256^3} = 64 \). This problem covers important mathematical concepts like exponents, radicals, and rational exponents. Suitable for high school students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation