In that compounds `KMnO_(4) and K_(2)Cr_(2)O_(7)` the highest oxidation state the element:

Explanation

To determine the highest oxidation state of the elements in the compounds KMnO4 and K2Cr2O7, we will calculate the oxidation states of manganese (Mn) and chromium (Cr) respectively.

### Step 1: Determine the oxidation state of manganese in KMnO4

1. **Identify the known oxidation states:**
- Potassium (K) has an oxidation state of +1.
- Oxygen (O) has an oxidation state of -2.

2. **Set up the equation:**
- The formula for KMnO4 consists of 1 potassium, 1 manganese, and 4 oxygen atoms. The total charge of the compound is 0.
- Let the oxidation state of manganese be \( x \).
- The equation can be set up as follows:
\[ +1 + x + 4(-2) = 0 \]

3. **Solve the equation:**
\[ +1 + x - 8 = 0 \]
\[ x - 7 = 0 \]
\[ x = +7 \]

4. **Conclusion:**
- The oxidation state of manganese in KMnO4 is +7.

### Step 2: Determine the oxidation state of chromium in K2Cr2O7

1. **Identify the known oxidation states:**
- Potassium (K) has an oxidation state of +1.
- Oxygen (O) has an oxidation state of -2.

2. **Set up the equation:**
- The formula for K2Cr2O7 consists of 2 potassium, 2 chromium, and 7 oxygen atoms. The total charge of the compound is 0.
- Let the oxidation state of chromium be \( y \).
- The equation can be set up as follows:
\[ 2(+1) + 2y + 7(-2) = 0 \]

3. **Solve the equation:**
\[ 2 + 2y - 14 = 0 \]
\[ 2y - 12 = 0 \]
\[ 2y = 12 \]
\[ y = +6 \]

4. **Conclusion:**
- The oxidation state of chromium in K2Cr2O7 is +6.

### Final Answer:
- The highest oxidation state among the elements in the compounds is +7 for manganese in KMnO4.

### Summary:
- In KMnO4, the highest oxidation state is +7 (Manganese).
- In K2Cr2O7, the highest oxidation state is +6 (Chromium).