Final answer:
To simplify the given expression, (5³)/(10x³)(3x²y)(10x(5)y³), we can break it down into numerator and denominator parts and simplify each separately. By applying the rules of exponentiation, we can simplify the expression to (125)/(1500x⁶y⁷).
Step-by-step explanation:
To simplify the expression (5³)/(10x³)(3x²y)(10x(5)y³), we can first simplify the numerator and the denominator separately.
The numerator, (5³), can be simplified to 5 × 5 × 5 = 125.
The denominator, (10x³)(3x²y)(10x(5)y³), can be simplified as follows:
- (10x³) can be written as 10 × x × x × x = 10x³
- (3x²y) remains as it is
- (10x(5)y³) can be written as 10 × x × (5 × y) × y × y × y = 10xy³ × 5y³ = 50xy³y³ = 50xy⁶
Now, we simplify the expression by dividing the numerator by the denominator:
(125)/(10x³)(3x²y)(10x(5)y³) = 125/(10x³)(3x²y)(50xy⁶) = (125)/(10x³ × 3x²y × 50xy⁶).
We can simplify the expression further by combining like terms:
(125)/(10 × 3 × 50)(x³ × x² × x × y × xy⁶) = (125)/(1500x⁶y⁷).
Therefore, the simplified expression is (125)/(1500x⁶y⁷).