Final Answer:
To express 4^1/2 as a quotient of two integers, it can be written as 9/2.
Step-by-step explanation:
To convert 4^1/2 into a quotient of two integers, we recognize that 4^1/2 is the same as 4 + 1/2. To represent the mixed number as a fraction, multiply the whole number (4) by the denominator of the fraction (2) and add the numerator (1). This gives 4^1/2 as 9/2. Therefore, 4^1/2 can be expressed as the quotient of two integers: 4^1/2 = 9/2.
In the fraction 9/2, the numerator (9) represents the total number of parts, and the denominator (2) represents the size of each part. This means that 4^1/2 is equivalent to having 9 parts, each of size 1/2. The conversion to a quotient of two integers is a way to represent this quantity in a more concise form, facilitating mathematical operations and comparisons.
In conclusion, 4^1/2 can be expressed as the quotient of two integers by recognizing its equivalence to 9/2. This conversion provides a clear representation of the mixed number as a fraction, making it easier to work with in various mathematical contexts.