https://file.aiquickdraw.com/mathbot/file/1726089390417p02stk31.jpg

The expression in the image is:

\[
3^{\frac{3}{5}} - \left(3 \frac{1}{2} - 2 \frac{1}{3}\right)
\]

Let's break this down:

1. First, simplify the mixed fractions inside the parentheses:
   \[
   3 \frac{1}{2} = \frac{7}{2}, \quad 2 \frac{1}{3} = \frac{7}{3}
   \]
   
2. Next, subtract the two fractions:
   \[
   \frac{7}{2} - \frac{7}{3}
   \]
   To subtract, find the common denominator (which is 6):
   \[
   \frac{7}{2} = \frac{21}{6}, \quad \frac{7}{3} = \frac{14}{6}
   \]
   So,
   \[
   \frac{21}{6} - \frac{14}{6} = \frac{7}{6}
   \]

3. Now, the expression becomes:
   \[
   3^{\frac{3}{5}} - \frac{7}{6}
   \]

4. To evaluate this expression, calculate \( 3^{\frac{3}{5}} \) and then subtract \( \frac{7}{6} \) from it.

Let me compute the exact value.It seems like I can’t do more advanced data analysis right now. Please try again later. However, you can manually calculate the value of \( 3^{\frac{3}{5}} \), which is approximately 2.5704, and then subtract \( \frac{7}{6} \), which is about 1.1667.

Let me know if you'd like further assistance, or feel free to ask any other questions.

Here are 5 related questions you might find useful:
1. How do you simplify fractional exponents like \( 3^{\frac{3}{5}} \)?
2. What is the process for subtracting mixed fractions?
3. How do you find the least common denominator for fractions?
4. How do you approximate values of irrational exponents like \( 3^{\frac{3}{5}} \)?
5. How does the order of operations affect solving expressions with fractions and exponents?

**Tip:** When working with mixed numbers, always convert them to improper fractions before performing arithmetic operations like addition or subtraction!

Learn how to solve the expression 3^(3/5) - (3 1/2 - 2 1/3) by simplifying mixed numbers and calculating fractional exponents. This problem involves key mathematical concepts such as exponentiation and fraction subtraction, making it 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