(729 power 3 / 729) close divided by 3 power 8
The Correct Answer and Explanation is:
Let’s solve the expression step by step:
Given:
(7293729)÷38\left(\frac{729^3}{729}\right) \div 3^8(7297293)÷38
Step 1: Simplify the fraction inside the parentheses
7293729=7293−1=7292\frac{729^3}{729} = 729^{3 – 1} = 729^27297293=7293−1=7292
Step 2: Express 729 as a power of 3
729=36729 = 3^6729=36
So: 7292=(36)2=312729^2 = (3^6)^2 = 3^{12}7292=(36)2=312
Step 3: Divide by 383^838
31238=312−8=34\frac{3^{12}}{3^8} = 3^{12 – 8} = 3^438312=312−8=34
Step 4: Evaluate the final power
34=813^4 = 8134=81
✅ Final Answer: 81
Explanation:
The problem involves simplifying a compound expression using the rules of exponents. The original expression is: (7293729)÷38\left(\frac{729^3}{729}\right) \div 3^8(7297293)÷38
The first part is a fraction where the same base number is raised to a power in the numerator and without a power in the denominator. When dividing terms with the same base, you subtract the exponents. In this case: 7293729=7293−1=7292\frac{729^3}{729} = 729^{3 – 1} = 729^27297293=7293−1=7292
To proceed, we need to express 729 in terms of a prime base. The number 729 is a power of 3. By calculating or knowing from experience: 36=7293^6 = 72936=729
So: 7292=(36)2=36×2=312729^2 = (3^6)^2 = 3^{6 \times 2} = 3^{12}7292=(36)2=36×2=312
Now, the full expression becomes: 312÷383^{12} \div 3^8312÷38
Again, when dividing exponents with the same base, subtract the exponents: 312−8=343^{12 – 8} = 3^4312−8=34
Finally, calculate: 34=3×3×3×3=813^4 = 3 \times 3 \times 3 \times 3 = 8134=3×3×3×3=81
This shows how simplifying powers using exponent laws helps reduce complex expressions to basic numbers. The final answer is 81.
