https://file.aiquickdraw.com/mathbot/file/1727326134215bitkm8xm.jpg

The equation in the image is:

\[
\frac{5^4}{9} \cdot \frac{1^2}{3} - \left( \frac{2}{3} - \frac{1}{5} \right)
\]

Let's break it down step-by-step:

### Step 1: Simplify \( \frac{5^4}{9} \cdot \frac{1^2}{3} \)

- \( 5^4 = 625 \)
- \( 1^2 = 1 \)

So, this part becomes:

\[
\frac{625}{9} \cdot \frac{1}{3} = \frac{625}{27}
\]

### Step 2: Simplify \( \left( \frac{2}{3} - \frac{1}{5} \right) \)

To subtract these fractions, we need a common denominator. The least common denominator (LCD) of 3 and 5 is 15.

\[
\frac{2}{3} = \frac{10}{15}, \quad \frac{1}{5} = \frac{3}{15}
\]

Now subtract:

\[
\frac{10}{15} - \frac{3}{15} = \frac{7}{15}
\]

### Step 3: Final expression

Now, the whole expression is:

\[
\frac{625}{27} - \frac{7}{15}
\]

To subtract these fractions, find the least common denominator between 27 and 15, which is 135. We convert both fractions:

\[
\frac{625}{27} = \frac{3125}{135}, \quad \frac{7}{15} = \frac{63}{135}
\]

Now subtract:

\[
\frac{3125}{135} - \frac{63}{135} = \frac{3062}{135}
\]

This is the simplified result. 

Would you like more details or further clarification?

Here are some related questions you might find useful:
1. What is the general rule for multiplying fractions?
2. How do you find the least common denominator?
3. What are the properties of exponents?
4. How do you convert improper fractions into mixed numbers?
5. How can you verify your answer when working with fractions?

**Tip:** Always simplify fractions as much as possible for clarity and accuracy.

Simplify the following expression: \( \frac{5^4}{9} \cdot \frac{1^2}{3} - \left( \frac{2}{3} - \frac{1}{5} \right) \)

This problem involves simplifying an expression with exponentiation, multiplication, and subtraction of fractions. Learn how to solve step-by-step and understand key concepts like the properties of exponents, multiplying fractions, and finding the least common denominator. Suitable for students in Grades 7-9.

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