{ 3  ^ { 8  }    }{ 3  ^ { 5  }    }  +(2  ^ { 3  }   \times  2 \times  2  ^ { 2  }  )-(4)  ^ { 3  }  --435  ^ { 0  }   

Let's break down and solve the given expression:

\[
\text{{Expression: }} \{ 3 ^ {8} \} \{ 3 ^ {5} \} + (2 ^ {3} \times 2 \times 2 ^ {2}) - (4) ^ {3} -- 435 ^ {0}
\]

1. **Simplify each part**:
   - \(\{ 3 ^ {8} \} \{ 3 ^ {5} \}\): 
     \[
     3^8 \times 3^5 = 3^{8+5} = 3^{13}
     \]
   - \((2 ^ {3} \times 2 \times 2 ^ {2})\):
     \[
     2^3 \times 2 \times 2^2 = 8 \times 2 \times 4 = 64
     \]
   - \((4) ^ {3}\):
     \[
     4^3 = 64
     \]
   - \(435 ^ {0}\):
     \[
     435^0 = 1 \text{ (Any non-zero number raised to the power of 0 is 1)}
     \]

2. **Substitute the simplified values into the expression**:
   \[
   3^{13} + 64 - 64 + 1
   \]

3. **Combine and simplify**:
   \[
   3^{13} + (64 - 64) + 1 = 3^{13} + 0 + 1 = 3^{13} + 1
   \]

4. **Calculate \(3^{13}\)**:
   \[
   3^{13} = 1594323
   \]
   
   So, the expression simplifies to:
   \[
   1594323 + 1 = 1594324
   \]

The final answer is \( \boxed{1594324} \).

Would you like more details or have any questions?

### Related Questions:
1. What is the general rule for multiplying powers of the same base?
2. How do you simplify expressions with mixed operations and exponents?
3. What happens when any number is raised to the power of 0?
4. How do you solve an expression involving both addition and subtraction of exponential terms?
5. Can you show the step-by-step process to manually calculate \(3^{13}\)?

**Tip:** When dealing with exponents, always remember the laws of exponents, such as \(a^m \times a^n = a^{m+n}\). This will simplify your calculations significantly.

{ 3  ^ { 8  }    }{ 3  ^ { 5  }    }  +(2  ^ { 3  }   \times  2 \times  2  ^ { 2  }  )-(4)  ^ { 3  }  --435  ^ { 0  }

Learn how to simplify the expression { 3^8 }{ 3^5 } + (2^3 × 2 × 2^2) - 4^3 - 435^0 with a detailed step-by-step breakdown. This example covers key exponent rules, including multiplying powers with the same base and calculating numbers raised to zero power. Suitable for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation