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.

$M = 80 \left(\frac{1}{2}\right)^{9/3} = 80 \left(\frac{1}{2}\right)^3 = 80 \times \frac{1}{8} = 10$

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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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: