solve 3 x (7 to the power of 2) x (11 to the power of 8) / (21 x (11 to the power of 3)) answer in exponential form

To solve the expression \( \frac{3 \times 7^2 \times 11^8}{21 \times 11^3} \) and simplify it in exponential form, follow these steps:

1. **Factor the denominator**:
   \[
   21 = 3 \times 7
   \]
   So the expression becomes:
   \[
   \frac{3 \times 7^2 \times 11^8}{3 \times 7 \times 11^3}
   \]

2. **Cancel out the common factors**:
   - The \(3\) in the numerator and denominator cancel out.
   - The \(7\) in the numerator and denominator cancel out, leaving \(7^{2-1} = 7^1\) in the numerator.

   This simplifies the expression to:
   \[
   \frac{7^1 \times 11^8}{11^3}
   \]

3. **Simplify the powers of 11**:
   \[
   \frac{11^8}{11^3} = 11^{8-3} = 11^5
   \]

   So the expression simplifies further to:
   \[
   7 \times 11^5
   \]

Thus, the final simplified answer in exponential form is \( 7 \times 11^5 \).

Would you like more details on any of these steps or have any questions?

### Related Questions:
1. How do you simplify expressions involving exponents?
2. What are the rules for multiplying and dividing exponents?
3. Can you explain how to handle exponents when the base numbers are different?
4. How do you factor complex expressions in algebra?
5. What are the properties of exponents that help simplify expressions?

### Tip:
Always remember to cancel out common factors in both the numerator and denominator before simplifying powers, as it makes the calculations easier and reduces the chances of mistakes.

Learn how to solve the expression 3 x (7^2) x (11^8) / (21 x (11^3)) and simplify it in exponential form. This problem involves advanced concepts in exponents and simplifying algebraic expressions. Suitable for high school students studying advanced algebra.

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