Simplify `12^((2)/(5)). 5^((2)/(5))`

Answer

To simplify the expression \( 12^{\frac{2}{5}} \cdot 5^{\frac{2}{5}} \), we can follow these steps:

### Step 1: Identify the common exponent
We notice that both terms have the same exponent, which is \( \frac{2}{5} \).

### Step 2: Combine the bases
Since the bases are different but the exponents are the same, we can combine them using the property of exponents:
\[ a^m \cdot b^m = (a \cdot b)^m \]
Applying this property, we can rewrite the expression as:
\[ (12 \cdot 5)^{\frac{2}{5}} \]

### Step 3: Calculate the product of the bases
Now, we calculate the product of the bases:
\[ 12 \cdot 5 = 60 \]

### Step 4: Write the expression with the new base
Now we can rewrite our expression:
\[ 60^{\frac{2}{5}} \]

### Step 5: Final expression
Thus, the simplified form of \( 12^{\frac{2}{5}} \cdot 5^{\frac{2}{5}} \) is:
\[ 60^{\frac{2}{5}} \]