## Simplifying the Expression: (5x²y)²(2xy³z)³(4xyz)

This expression involves multiple variables with exponents and requires careful application of the rules of exponents to simplify it. Let's break down the process step-by-step.

### Applying the Exponent Rule for Parentheses

First, we need to apply the exponent rule that states **(a^m)^n = a^(m*n)** to the individual terms within the parentheses.

**(5x²y)² = 5²x^(2*2)y² = 25x⁴y²****(2xy³z)³ = 2³x³y^(3*3)z³ = 8x³y⁹z³**

Now our expression looks like this: **25x⁴y²(8x³y⁹z³)(4xyz)**

### Multiplying the Terms

Next, we multiply the coefficients and combine the variables with the same base by adding their exponents. Remember **a^m * a^n = a^(m+n)**

**25 * 8 * 4 = 800****x⁴ * x³ * x = x⁸****y² * y⁹ * y = y¹²****z³ * z = z⁴**

Finally, we put it all together: **800x⁸y¹²z⁴**

### Simplified Expression

The simplified form of the expression **(5x²y)²(2xy³z)³(4xyz)** is **800x⁸y¹²z⁴**.