Final answer:
The expression 27xy⁷/x⁸y² simplifies to 27y⁵/x⁷ after subtracting the exponents of the same base and leaving only positive exponents.
Step-by-step explanation:
To simplify the expression 27xy⁷ divided by x⁸y² using only positive exponents, we should follow the rules of exponents for division. When dividing powers with the same base, you subtract the exponents. So, we simplify the expression as follows:
- Divide the coefficients: 27 divided by 1 is 27.
- Subtract the exponents of x: 1 - 8 = -7 (since we want only positive exponents, we write this as x⁰/6C⁷, and since x⁰ is equal to 1, we leave only the denominator).
- Subtract the exponents of y: 7 - 2 = 5.
So the expression simplifies to 27y⁵/x⁷.