Write the following expressions in standard form. $$ 3\cdot x\cdot x\cdot y\cdot2\cdot y\cdot z\cdot z\cdot2 $$

To write the expression $ 3 \cdot x \cdot x \cdot y \cdot 2 \cdot y \cdot z \cdot z \cdot 2 $ in standard form, follow these steps:

### Step 1: Rearrange the terms
Group the constants and variables together:
\[
3 \cdot 2 \cdot 2 \cdot x \cdot x \cdot y \cdot y \cdot z \cdot z
\]

### Step 2: Multiply the constants
\[
3 \cdot 2 \cdot 2 = 12
\]

### Step 3: Use exponents for repeated variables
- $ x \cdot x = x^2 $
- $ y \cdot y = y^2 $
- $ z \cdot z = z^2 $

### Step 4: Combine everything into standard form
\[
12x^2y^2z^2
\]

So, the standard form of the given expression is:
\[
12x^2y^2z^2
\]

Do you need more details or have any questions?

Here are five related questions to expand the concept:
1. How would you write $ 5 \cdot x \cdot x \cdot x \cdot y \cdot y \cdot 4 $ in standard form?
2. What is the standard form of $ 7 \cdot a \cdot a \cdot b \cdot b \cdot 3 \cdot b \cdot c \cdot c $?
3. Simplify $ 4 \cdot x^2 \cdot y \cdot y \cdot z^2 \cdot 3 \cdot x $.
4. If $ 2 \cdot x \cdot x \cdot x \cdot 2 \cdot y \cdot z^3 $ is given, what is its standard form?
5. Write the expression $ 6 \cdot a \cdot a \cdot b \cdot b \cdot c \cdot c $ in terms of exponents.

**Tip:** Always combine constants first and use exponents to represent repeated variables for standard form expressions.

Write the following expressions in standard form. $$ 3\cdot x\cdot x\cdot y\cdot 2\cdot y\cdot z\cdot z\cdot 2 $$

Learn how to simplify the expression 3x^2y^2z^2 by multiplying constants and combining like terms using exponents. This problem is ideal for students in Grades 6-8, covering basic algebra and exponentiation.

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