19+\left(13-7\right)\cdot\left(3\right)^{2}-11

Let's solve the expression step by step:

Given expression:

\[
19 + \left(13 - 7\right) \cdot \left(3\right)^{2} - 11
\]

1. **Simplify inside the parentheses**:
   \[
   13 - 7 = 6
   \]
   
   Now the expression becomes:
   \[
   19 + 6 \cdot \left(3\right)^{2} - 11
   \]

2. **Evaluate the exponent**:
   \[
   3^2 = 9
   \]
   
   Now the expression is:
   \[
   19 + 6 \cdot 9 - 11
   \]

3. **Multiply**:
   \[
   6 \cdot 9 = 54
   \]
   
   Now the expression becomes:
   \[
   19 + 54 - 11
   \]

4. **Perform the addition and subtraction from left to right**:
   \[
   19 + 54 = 73
   \]
   \[
   73 - 11 = 62
   \]

So, the value of the expression is:

\[
\boxed{62}
\]

Would you like further details or have any questions about this solution?

Here are some related questions:
1. How would you solve the expression \(18 + (12 - 4) \times (2)^2 - 10\)?
2. What happens if you change the base of the exponent from 3 to 4 in the original problem?
3. Can you simplify the expression \(15 + (10 - 5) \times (4)^{2} - 8\)?
4. How do you evaluate \(20 + (14 - 6) \times (5)^{2} - 12\)?
5. What is the result of \(21 + (16 - 9) \times (2)^{3} - 7\)?

**Tip:** Always follow the order of operations: parentheses, exponents, multiplication and division (from left to right), and then addition and subtraction (from left to right).

Learn how to solve the expression 19 + (13 - 7) * (3)^2 - 11 step by step with detailed explanations. This problem covers key math concepts including order of operations, parentheses simplification, exponentiation, and addition/subtraction. Suitable for Grades 6-8.

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