`(a)/(b) : (c )/(d) : (e )/(f)=(2)/(3)`
`(m^(2)a+n^(2)c+p^(2)e)/(m^(2)b+n^(2)d+p^(2)f)=`
`(m^(2)a-3^(2)c-2^(2)e)/(m^(2)b-3^(2)d-2^(2)f)=`

Answer

To solve the problem step by step, we will start by interpreting the given ratios and then substituting the values into the expressions provided.

### Step 1: Understand the Ratios
We are given the ratios:
\[ \frac{a}{b} : \frac{c}{d} : \frac{e}{f} = \frac{2}{3} \]
This means:
\[ \frac{a}{b} = \frac{2}{3}, \quad \frac{c}{d} = \frac{2}{3}, \quad \frac{e}{f} = \frac{2}{3} \]

### Step 2: Express Variables in Terms of k
From the ratios, we can express \(a\), \(b\), \(c\), \(d\), \(e\), and \(f\) in terms of a common variable \(k\):
- Let \(a = 2k\)
- Let \(b = 3k\)
- Let \(c = 2k\)
- Let \(d = 3k\)
- Let \(e = 2k\)
- Let \(f = 3k\)

### Step 3: Substitute into the First Expression
Now we substitute these values into the first expression:
\[ \frac{m^2 a + n^2 c + p^2 e}{m^2 b + n^2 d + p^2 f} \]
Substituting the values:
\[ = \frac{m^2(2k) + n^2(2k) + p^2(2k)}{m^2(3k) + n^2(3k) + p^2(3k)} \]

### Step 4: Factor Out k
Now we can factor out \(k\) from both the numerator and the denominator:
\[ = \frac{2k(m^2 + n^2 + p^2)}{3k(m^2 + n^2 + p^2)} \]

### Step 5: Simplify the Expression
Since \(k\) is common in both the numerator and the denominator, we can cancel it out:
\[ = \frac{2(m^2 + n^2 + p^2)}{3(m^2 + n^2 + p^2)} \]
This simplifies to:
\[ = \frac{2}{3} \]

### Step 6: Final Result
Thus, the value of the expression is:
\[ \frac{2}{3} \]