https://file.aiquickdraw.com/mathbot/file/172706127109702o7kkn9.jpg

Let's break down and solve the given expression step by step. The expression in the image is:

\[
\frac{11^2 - 8^2}{(11 + 8)} \times \frac{1}{27} - 3^{-2}
\]

### Step 1: Simplify the powers
- \(11^2 = 121\)
- \(8^2 = 64\)
- \(3^{-2} = \frac{1}{3^2} = \frac{1}{9}\)

So the expression becomes:

\[
\frac{121 - 64}{(11 + 8)} \times \frac{1}{27} - \frac{1}{9}
\]

### Step 2: Simplify inside the parentheses and the fraction
- \(121 - 64 = 57\)
- \(11 + 8 = 19\)

Now the expression is:

\[
\frac{57}{19} \times \frac{1}{27} - \frac{1}{9}
\]

### Step 3: Multiply the fractions
- \(\frac{57}{19} \times \frac{1}{27} = \frac{57}{19 \times 27} = \frac{57}{513}\)

So now the expression is:

\[
\frac{57}{513} - \frac{1}{9}
\]

### Step 4: Find a common denominator
To subtract these fractions, we need a common denominator. The least common denominator of 513 and 9 is 513. We rewrite \(\frac{1}{9}\) as:

\[
\frac{1}{9} = \frac{57}{513}
\]

Now the expression becomes:

\[
\frac{57}{513} - \frac{57}{513}
\]

### Step 5: Subtract the fractions
\[
\frac{57 - 57}{513} = \frac{0}{513} = 0
\]

Thus, the final result is:

\[
0
\]

Would you like any further clarification or details on any step?

### 5 Related Questions:
1. How do you find the least common denominator in fraction subtraction?
2. What are the rules for multiplying fractions?
3. How do negative exponents work, and why is \(3^{-2} = \frac{1}{9}\)?
4. Can you explain how to simplify an expression involving powers of numbers?
5. What is the general method for simplifying complex fractions?

**Tip:** When solving problems with multiple steps, solving powers and parentheses first helps reduce the complexity!

Simplify the expression (11^2 - 8^2) / (11 + 8) * (1 / 27) - 3^-2

This step-by-step guide simplifies the expression (11^2 - 8^2) / (11 + 8) * (1/27) - 3^-2 using exponent rules, fraction operations, and algebraic simplification. Suitable for Grade 9 students.

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