Final answer:
Dividing (25x)/(2a) by (5x)/(4a^(4)x^(5)) involves flipping the second fraction and multiplying it with the first. After simplifying by cancelling out common factors, the answer is 10a^(3)x^(4).
Step-by-step explanation:
To divide the expression (25x)/(2a) by (5x)/(4a4x5), we use the rule that dividing by a fraction is the same as multiplying by its reciprocal. This means we will flip the second fraction and multiply it with the first fraction.
First, express the problem as a multiplication of the first expression and the reciprocal of the second:
- Write the given division problem: (25x)/(2a) ÷ (5x)/(4a4x5)
- Flip the second fraction to get its reciprocal: (4a4x5)/(5x).
- Multiply the first expression by this reciprocal: (25x)/(2a) × (4a4x5)/(5x).
Simplify the expression by cancelling out the common factors:
- x in the numerator of the first fraction and x in the denominator of the second fraction can be reduced.
- The numerical factor 5 in the denominator of the second fraction and 25 in the numerator of the first fraction cancel out to a factor of 5.
The resulting simplified expression is:
(25x)/(2a) × (4a4x5)/(5x) = (5 × 4a4x4)/(2a)
Which further simplifies to:
(20a^4x^4)/(2a) = 10a^3x^4