Write down the following in product form:
`6 p^(2)q^(3)y^(4)`.

Answer

To write the expression \( 6p^2q^3y^4 \) in product form, we will break down each term into its factors. Here are the steps:

### Step 1: Identify the coefficients and variables
The expression consists of a coefficient \( 6 \) and the variables \( p \), \( q \), and \( y \) raised to their respective powers.

### Step 2: Write the coefficient as a product
The coefficient \( 6 \) can be expressed as the product of its prime factors:
\[ 6 = 2 \times 3 \]

### Step 3: Expand the variables
Now, we will expand each variable according to its exponent:
- \( p^2 \) means \( p \times p \)
- \( q^3 \) means \( q \times q \times q \)
- \( y^4 \) means \( y \times y \times y \times y \)

### Step 4: Combine all factors
Now, we can combine all the factors together:
\[ 6p^2q^3y^4 = (2 \times 3) \times (p \times p) \times (q \times q \times q) \times (y \times y \times y \times y) \]

### Step 5: Write the final product form
Putting it all together, we have:
\[ 6p^2q^3y^4 = 2 \times 3 \times p \times p \times q \times q \times q \times y \times y \times y \times y \]

Thus, the product form of \( 6p^2q^3y^4 \) is:
\[ 2 \times 3 \times p \times p \times q \times q \times q \times y \times y \times y \times y \]