%5E2(2xy%5E3z)%5E3(4xyz)-simplified.jpeg "(5x^2y)^2(2xy^3z)^3(4xyz) Simplified")
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.