Final answer:
To simplify the expression 15x⁹y⁶ / 3x⁴y⁶, divide the numerical coefficients to get 5, and subtract the exponents of like bases to get x⁵, with y terms cancelling out since y⁰ equals 1, resulting in 5x⁵.
Step-by-step explanation:
To simplify the expression you provided (15x⁹y⁶ / 3x⁴y⁶), start by separating the numerical coefficients and the variables with exponents.
First, divide the numbers: 15 / 3 = 5.
Next, apply the exponent rules to the variables. For x, subtract the exponents (since they have the same base and are being divided): x⁹ / x⁴ = x⁹-⁴ = x⁵. For y, they have the same exponents and base, which also means division leads to cancelling out: y⁶ / y⁶ = y⁶-⁶ = y⁰. Remember, any number (including y) raised to the power of 0 equals 1.
The simplified expression is therefore 5x⁵.
To simplify the expression 15x⁹y⁶ / 3x⁴y⁶, we can divide the numbers (15 / 3 = 5) and the variables (x⁹ / x⁴ = x⁵) and (y⁶ / y⁶ = y⁰ = 1). The simplified expression is 5x⁵.