Find the product of `6xy and 7x^(2)`

Answer

To find the product of \(6xy\) and \(7x^2\), we will follow these steps:

### Step 1: Write down the expression
We need to multiply the two expressions:
\[ 6xy \times 7x^2 \]

### Step 2: Multiply the coefficients (constants)
First, we multiply the numerical coefficients (the constants) together:
\[ 6 \times 7 = 42 \]

### Step 3: Multiply the variables
Next, we multiply the variables. We have \(x\) and \(x^2\):
- The exponent of \(x\) in \(6xy\) is \(1\) (since \(x\) is the same as \(x^1\)).
- The exponent of \(x\) in \(7x^2\) is \(2\).

When multiplying variables with the same base, we add their exponents:
\[ x^1 \times x^2 = x^{1+2} = x^3 \]

### Step 4: Include the remaining variable
Now, we also have the variable \(y\) from the term \(6xy\). Since there is no \(y\) in \(7x^2\), we simply keep \(y\) as it is.

### Step 5: Combine all parts
Putting it all together, we have:
\[ 42x^3y \]

### Final Answer
Thus, the product of \(6xy\) and \(7x^2\) is:
\[ \boxed{42x^3y} \]

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