Understanding the Expression
To simplify the expression (2^3 × 2^5) ÷ 2^4, we first need to apply the laws of exponents. The laws of exponents state that when multiplying like bases, we add the exponents, and when dividing, we subtract the exponents.
Step 1: Multiply the Terms Together
- The expression starts with 2^3 × 2^5.
- According to the multiplication rule: a^m × a^n = a^(m+n).
- Here, we have:
- 2^3 × 2^5 = 2^(3+5) = 2^8.
Step 2: Divide by the Last Term
- Now we have 2^8 ÷ 2^4.
- According to the division rule: a^m ÷ a^n = a^(m-n).
- Thus, we can write:
- 2^8 ÷ 2^4 = 2^(8-4) = 2^4.
Final Result
- After simplifying, we arrive at 2^4.
- Evaluating 2^4 gives us 16.
Conclusion
- The simplified form of the original expression (2^3 × 2^5) ÷ 2^4 is:
- 16.
This approach illustrates how to effectively use exponent rules to simplify expressions, which is crucial for solving problems in mathematics and competitive exams like UPSC.