Final answer:
To fully simplify the given expression (10x⁶y⁷)/(4x⁷y²), divide the coefficients and subtract the exponents for each variable. The fully simplified expression is 2x⁻¹y⁵.
Step-by-step explanation:
To fully simplify the expression (10x⁶y⁷)/(4x⁷y²), we can divide the coefficients and subtract the exponents for each variable. Dividing 10 by 4 gives us 2. For the variable x, subtracting the exponents 6 and 7 gives us x⁻¹. And for the variable y, subtracting the exponents 7 and 2 gives us y⁵. Therefore, the fully simplified expression is 2x⁻¹y⁵.