3/2 to the power of 2 as fraction in simplest form
The Correct Answer and Explanation is :
The correct answer is: {9}{4}
To simplify the expression ( \left(\frac{3}{2}\right)^2 ) and express it as a fraction in simplest form, we start by applying the power of a fraction.
Step 1: Apply the Power of a Fraction
When you raise a fraction to a power, you raise both the numerator and the denominator to that power. For our expression:
[
\left(\frac{3}{2}\right)^2 = \frac{3^2}{2^2}
]
Step 2: Calculate the Numerator and Denominator
Now we calculate the squares of the numerator and denominator:
- Numerator:
[
3^2 = 3 \times 3 = 9
] - Denominator:
[
2^2 = 2 \times 2 = 4
]
So, we can now rewrite the expression:
[
\left(\frac{3}{2}\right)^2 = \frac{9}{4}
]
Step 3: Simplify the Fraction
In this case, the fraction ( \frac{9}{4} ) is already in simplest form because there are no common factors between the numerator (9) and the denominator (4). The number 9 can be factored into ( 3 \times 3 ), while 4 can be factored into ( 2 \times 2 ). Since these factors share no common prime factors, we conclude that ( \frac{9}{4} ) is the simplest form of the fraction.
Conclusion
Thus, ( \left(\frac{3}{2}\right)^2 ) simplifies to ( \frac{9}{4} ). This result indicates that when you square ( \frac{3}{2} ), you obtain ( \frac{9}{4} ), which is an improper fraction. Improper fractions, like ( \frac{9}{4} ), can also be expressed as mixed numbers. In this case, ( \frac{9}{4} = 2 \frac{1}{4} ) if desired. However, the simplest form as a fraction is ( \frac{9}{4} ).