https://file.aiquickdraw.com/mathbot/file/17265071048765ecuvgxf.jpg

The task in the image asks to express the roots as powers with rational exponents. Here's how we can convert each root into a rational exponent:

1. \( \sqrt[2]{6} = 6^{\frac{1}{2}} \)
2. \( \sqrt[4]{10} = 10^{\frac{1}{4}} \)
3. \( \sqrt[3]{5} = 5^{\frac{1}{3}} \)
4. \( \sqrt[4]{2^3} = (2^3)^{\frac{1}{4}} = 2^{\frac{3}{4}} \)
5. \( \sqrt[5]{1.5^2} = (1.5^2)^{\frac{1}{5}} = 1.5^{\frac{2}{5}} \)
6. \( \sqrt[6]{0.3^3} = (0.3^3)^{\frac{1}{6}} = 0.3^{\frac{3}{6}} = 0.3^{\frac{1}{2}} \)

These are the expressions of the given roots in terms of rational exponents.

Would you like further explanations on any of these conversions?

Here are some related questions for practice:
1. How do you convert \( \sqrt[3]{x^4} \) into a rational exponent?
2. What is the value of \( 9^{\frac{1}{2}} \)?
3. How would you simplify \( \left( x^{\frac{2}{3}} \right)^3 \)?
4. What is the difference between a square root and a cube root in terms of exponents?
5. Can a negative number have a rational exponent?

**Tip**: When raising a power to another power, multiply the exponents!

Noteer de wortelvorm als een macht met een rationale exponent: √6, ⁴√10, ³√5, ⁴√2³, ⁵√1,5², ⁶√0,3³

Learn how to express roots like √6, ⁴√10, and others as rational exponents. This step-by-step guide covers key exponent rules, including how to convert roots into fractional exponents. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation