Let's solve the questions one at a time.
1. Simplify
Using the Product Rule of Exponents:
Answer:
2. Find the numerical equivalent of
Using the Property of Exponents:
Calculating
Answer:
3. What is the missing exponent in the equation ?
Using the Quotient Rule of Exponents:
Answer:
4. Simplify
Using the Quotient Rule of Exponents:
Answer:
5. What is the missing number in the expression ?
Using the Quotient Rule of Exponents:
Answer:
6. Evaluate
The expression
Calculating
Thus,
Keeping the answer in decimal is less clear, let's re-evaluate:
If simply to get value:
- Using direct calculation
When using in approximation close enough to: Converting more:
Answer:
7. Apply the Zero Power Rule.
Using the Zero Power Rule:
Answer:
8. Solve
Answer:
9. Simplify
Using the Power Rule of Exponents:
Answer:
10. Expand
The expanded equivalent expression for
Answer:
11. Simplify
Using the Power Rule:
Answer:
12. Simplify
Using the positive exponent property:
Answer:
13. Convert to positive exponents.
Answer:
14. Solve
Step 1: Convert to positive exponents:
Thus, simplifying:
Final Implied Answer: