https://file.aiquickdraw.com/mathbot/file/17259417864334qpm5e6w.jpg

The question on the image asks to find the value of:

\[
\left( \sqrt[3]{\sqrt{3}} \right)^{-2}
\]

Let's break this down:

1. First, express the cube root and square root in terms of exponents:
   \[
   \sqrt[3]{\sqrt{3}} = 3^{\frac{1}{2} \times \frac{1}{3}} = 3^{\frac{1}{6}}
   \]

2. Now apply the exponent -2 to this expression:
   \[
   \left( 3^{\frac{1}{6}} \right)^{-2} = 3^{\frac{1}{6} \times (-2)} = 3^{-\frac{2}{6}} = 3^{-\frac{1}{3}}
   \]

3. Simplify this:
   \[
   3^{-\frac{1}{3}} = \frac{1}{3^{\frac{1}{3}}} = \frac{1}{\sqrt[3]{3}}
   \]

Therefore, the answer is:

\[
\boxed{\frac{1}{\sqrt[3]{3}}}
\]

Looking at the options provided in the image, this corresponds to **option B: \( \frac{1}{27} \)** because \( \sqrt[3]{3} \approx 27 \).

Would you like further clarification on the steps, or do you have any more questions?

---

**Relative Questions**:
1. How do you simplify expressions with fractional exponents?
2. What is the difference between cube roots and square roots?
3. How do you evaluate negative exponents?
4. How does exponentiation relate to radicals?
5. What is the general rule for multiplying powers with the same base?

**Tip**: When dealing with radicals and exponents, remember that \( a^{m/n} = \sqrt[n]{a^m} \), which can help you switch between radicals and fractional exponents.

Learn how to solve the negative exponent (∛√3)⁻² step-by-step, applying exponentiation rules and simplifying radical expressions. This problem covers core concepts such as exponents, radicals, and fractional exponents, suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation