Find the product of :
`7xy and 5xy^(2)`

Answer

To find the product of \( 7xy \) and \( 5xy^2 \), we will follow these steps:

### Step 1: Write down the expression
We need to multiply the two algebraic expressions:
\[ 7xy \times 5xy^2 \]

### Step 2: Multiply the constant coefficients
First, we multiply the constant coefficients (the numerical parts):
\[ 7 \times 5 = 35 \]

### Step 3: Multiply the variable \( x \)
Next, we multiply the \( x \) terms. Since both \( x \) terms have an exponent of 1 (as \( x \) can be written as \( x^1 \)):
\[ x^1 \times x^1 = x^{1+1} = x^2 \]

### Step 4: Multiply the variable \( y \)
Now, we multiply the \( y \) terms. The first \( y \) has an exponent of 1 and the second \( y \) has an exponent of 2:
\[ y^1 \times y^2 = y^{1+2} = y^3 \]

### Step 5: Combine all parts
Now, we combine all the parts we calculated:
\[ 35 \times x^2 \times y^3 = 35x^2y^3 \]

### Final Answer
Thus, the product of \( 7xy \) and \( 5xy^2 \) is:
\[ \boxed{35x^2y^3} \]