Fully simplify using only positive exponents.
start fraction, 27, x, cubed, y, to the power 5 , divided by, 3, x, to the power 4 , y, squared, end fraction
3x
4
y
2
27x
3
y
5
To fully simplify the expression using only positive exponents, we can use the following rules:
1. When dividing two powers with the same base, subtract the exponents: x^a / x^b = x^(a-b).
2. When raising a power to another power, multiply the exponents: (x^a)^b = x^(a*b).
3. When dividing by a fraction, flip the fraction and multiply: a/b / c/d = a/b * d/c.
4. Any number raised to the power of 0 is equal to 1.
Using these rules, we can simplify the expression as follows:
(27x^3y^5) / (3x^4y^2)
= 27/3 * x^3/x^4 * y^5/y^2
= 9 * x^(3-4) * y^(5-2)
= 9 * x^(-1) * y^3
= 9 * y^3 / x
The fully simplified expression is 9y^3 / x.