Question

Verify using only positive exponents. (25x²y)/(125x⁴y⁴)

Answer 1

To verify the expression (25x²y)/(125x⁴y⁴) using only positive exponents, simplify the numerator and denominator separately, then divide and simplify the result.

Step-by-step explanation:

To verify the expression (25x²y)/(125x⁴y⁴) using only positive exponents, we can simplify using the rules of exponents.

1. First, simplify the numerator: 25x²y = (5²)(x²)(y).
2. Next, simplify the denominator: 125x⁴y⁴ = (5³)(x⁴)(y⁴).
3. Now divide the numerator by the denominator, keeping in mind that dividing a number by itself equals 1: (5²)(x²)(y) / (5³)(x⁴)(y⁴) = (5²/5³)(x²/x⁴)(y/y⁴).
4. Finally, simplify each fraction in the expression: (5²/5³) = 1/5, (x²/x⁴) = 1/x², and (y/y⁴) = 1/y³.

Therefore, the final simplified expression is: (25x²y)/(125x⁴y⁴) = (1/5)(1/x²)(1/y³) = 1 / (5x²y³).