Fully simplify using only positive exponents.

Question

start fraction, 5, x, y, divided by, 125, x, squared, y, to the power 5 , end fraction
125x
2
y
5

5xy
​

Answer 1

To fully simplify the expression (5xy)/(125x^2y^5) using only positive exponents, we can reduce the denominator first by factoring out common factors:

125 = 5^3
x^2 = x^(2-1) = x
y^5 = y^(5-3) = y^2

So the expression becomes:

(5xy)/(5^3xy^2)

Next, we can cancel out the common factors in the numerator and denominator:

(5xy)/(5^3xy^2) = (1*xy)/(1*5*5*5*xy^2)

Finally, the simplified expression is:

(1)/(5*5*5*y) = 1/(125y)