Multiply :
`-5cd^(2)` by `- 5cd^(2)`

Answer

To solve the multiplication of the algebraic expressions \(-5cd^2\) by \(-5cd^2\), we will follow these steps:

### Step 1: Identify the components
We have two expressions to multiply:
- First expression: \(-5cd^2\)
- Second expression: \(-5cd^2\)

### Step 2: Multiply the coefficients
The coefficients are \(-5\) and \(-5\). When we multiply two negative numbers, the result is positive:
\[ -5 \times -5 = 25 \]

### Step 3: Multiply the variables
Next, we multiply the variable parts:
- For \(c\): \(c \times c = c^2\)
- For \(d^2\): \(d^2 \times d^2 = d^{2+2} = d^4\) (using the property of exponents that states \(a^m \times a^n = a^{m+n}\))

### Step 4: Combine the results
Now, we combine the results from the coefficients and the variables:
\[ 25 \times c^2 \times d^4 = 25c^2d^4 \]

### Final Answer
Thus, the final result of multiplying \(-5cd^2\) by \(-5cd^2\) is:
\[ \boxed{25c^2d^4} \]