Suppose two students trying to make a new measurement system so that they can use it like a code measurement system and others do not understand it Instead of taking 1 kg, 1 m and 1 second, as basic unit they took unit of mass as `alpha` kg, the unit of length as `beta` m and unit of times as `gamma` second. They called power in new system as "Aakash", then find The value of `alpha` "Aakash" in watt.

Answer

To solve the problem, we need to find the value of "Aakash" in watts, given the new measurement system defined by the students. Let's break it down step by step.

### Step 1: Understand the Definition of Power
Power is defined as the work done per unit time. Mathematically, it can be expressed as:
\[ P = \frac{W}{t} \]
where \(P\) is power, \(W\) is work done, and \(t\) is time.

### Step 2: Express Work in Terms of Force and Displacement
Work can be expressed as the product of force and displacement:
\[ W = F \cdot x \]
where \(F\) is force and \(x\) is displacement.

### Step 3: Express Force in Terms of Mass and Acceleration
Force can be defined using Newton's second law:
\[ F = m \cdot a \]
where \(m\) is mass and \(a\) is acceleration.

### Step 4: Substitute Force into the Work Equation
Substituting the expression for force into the work equation gives:
\[ W = (m \cdot a) \cdot x \]

### Step 5: Substitute Acceleration and Displacement
Acceleration can be expressed as \(a = \frac{F}{m}\) or in terms of units as \(m/s^2\). Thus, we can write:
\[ W = m \cdot \left(\frac{x}{t^2}\right) \cdot x \]
This leads to:
\[ W = m \cdot x^2 / t^2 \]

### Step 6: Substitute Work into the Power Equation
Now substituting the expression for work back into the power equation:
\[ P = \frac{m \cdot x^2}{t^2} \cdot \frac{1}{t} = \frac{m \cdot x^2}{t^3} \]

### Step 7: Substitute the Units
In the new measurement system:
- Mass \(m\) is represented as \(\alpha\) kg
- Length \(x\) is represented as \(\beta\) m
- Time \(t\) is represented as \(\gamma\) seconds

Substituting these into the power equation gives:
\[ P = \frac{\alpha \cdot \beta^2}{\gamma^3} \]

### Step 8: Define "Aakash"
In the new system, they have defined power as "Aakash". Therefore:
\[ \text{Aakash} = \frac{\alpha \cdot \beta^2}{\gamma^3} \]

### Step 9: Express Aakash in Terms of Watts
Since 1 watt (W) is defined as \(1 \text{ kg} \cdot \text{m}^2/\text{s}^3\), we can express the relationship:
\[ \text{Aakash} = \alpha \cdot \beta^2 \cdot \gamma^{-3} \]

### Final Expression
Thus, the value of "Aakash" in watts is:
\[ \text{Aakash} = \alpha \cdot \beta^2 \cdot \gamma^{-3} \]

### Summary
The final answer is:
\[ \text{Aakash} = \alpha \cdot \beta^2 \cdot \gamma^{-3} \text{ (in watts)} \]