Fully simplify using only positive exponents.
21x^5y^2/14x^8y^3
To fully simplify the expression, we can use the rules of exponents to combine like terms in the numerator and denominator.
First, we can simplify the coefficient by dividing both 21 and 14 by their greatest common factor, which is 7.
21/14 becomes 3/2.
Next, we can use the rule of exponents which states that when dividing variables with the same base, we subtract the exponents.
So, x^5/x^8 becomes x^(5-8) which is x^(-3).
Similarly, y^2/y^3 becomes y^(2-3) which is y^(-1).
Putting it all together, the expression simplifies to:
(3/2) * (x^(-3)) * (y^(-1))
Finally, we can rewrite the expression using positive exponents by reciprocal.
This gives us:
(3/2) * (1/x^3) * (1/y)
Or, simplifying further:
3/(2x^3y)