M = 80 \left(\frac12\right)^9/3 = 80 \left(\frac12\right)^3 = 80 \times \frac18 = 10 - Groen Casting
Decoding the Exponent: M = 80 × (1/2)^(9/3) = 10 Explained
Decoding the Exponent: M = 80 × (1/2)^(9/3) = 10 Explained
Mathematics often hides powerful simplifications behind seemingly complex expressions. One such elegant example is the calculation:
M = 80 × (1/2)^(9/3) = 80 × (1/2)^3 = 80 × 1/8 = 10
Understanding the Context
This equation demonstrates how breaking down exponents and simplifying powers can reveal clear, practical results. In this article, we’ll explore step-by-step how the initial expression transforms into the final answer—and why this process matters in math and real-world applications.
Understanding the Base Expression: 80 × (1/2)^(9/3)
At first glance, the expression
80 × (1/2)^(9/3)
might appear intimidating due to the fractional exponent. But breaking it down reveals a step-by-step simplification that’s both accessible and instructive.
Key Insights
First, simplify the exponent 9/3:
(1/2)^(9/3) = (1/2)^3
Since dividing 9 by 3 yields 3, we rewrite the expression as:
80 × (1/2)^3
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📰 \cdot 9 \cdot 9 = 486 📰 Now impose the even-sum condition. 📰 Sum is even if number of odd addends is even (since even + even = even, odd + odd = even).Final Thoughts
Simplifying the Power of 1/2
Recall the fundamental rule of exponents:
(a^m)^n = a^(m×n)
Applying this property:
(1/2)^3 = (1/2) × (1/2) × (1/2) = 1/8
So the expression becomes:
80 × (1/8)
Final Calculation: Multiplying to Find M
Now perform the multiplication:
