Fully simplify using only positive exponents.
start fraction, 20, x, to the power 6 , y, to the power 5 , divided by, 8, x, to the power 6 , y, to the power 6 , end fraction
8x
6
y
6
20x
6
y
5
To simplify the expression, we can subtract the exponents of x and y in the denominator from the exponents of x and y in the numerator:
start fraction, 20, x, to the power 6 , y, to the power 5 , divided by, 8, x, to the power 6 , y, to the power 6 , end fraction
= start fraction, 20x^(6-6) * y^(5-6), divided by, 8, end fraction
= start fraction, 20x^0 * y^(-1), divided by, 8, end fraction
Since any number raised to the power of 0 is equal to 1, we can simplify further:
= start fraction, 20 * 1 * y^(-1), divided by, 8, end fraction
= start fraction, 20y^(-1), divided by, 8, end fraction
= start fraction, 5y^(-1), divided by, 2, end fraction
In positive exponent form, the simplified expression is:
5/2y^(-1) or 5/(2y)