Final Answer:
The quotient of (4z⁵) divided by (2z³) is 2z².
Step-by-step explanation:
To find the quotient of two expressions with variables and exponents, we follow these steps:
1. Find the common variable and exponent.
2. Divide the coefficient of the numerator by the coefficient of the denominator.
3. Divide the exponent of the common variable in the numerator by the exponent of the common variable in the denominator. The result will be a fraction with a whole number in the numerator and a whole number in the denominator. If this fraction is not in simplest form, continue factoring until it is.
Let's apply these steps to our problem:
(4z⁵) / (2z³)
1. Common variable: z
2. Coefficient of numerator divided by coefficient of denominator: 4/2 = 2
3. Exponent of z in numerator divided by exponent of z in denominator: 5/3 = 5/3 (cannot be simplified further)
So, our quotient is 2z². This expression tells us that if we have a quantity that is represented by z raised to the fifth power, and we divide it by a quantity that is represented by z raised to the third power, we get a result that is represented by z raised to the second power multiplied by 2.