(6/7) to the 2nd power
The Correct Answer and Explanation is :
To calculate ((\frac{6}{7})^2), you multiply (\frac{6}{7}) by itself:
[
(\frac{6}{7})^2 = \frac{6}{7} \times \frac{6}{7} = \frac{6 \times 6}{7 \times 7} = \frac{36}{49}
]
So, the answer is (\frac{36}{49}).
Explanation
When squaring a fraction, the process involves squaring both the numerator (the top part of the fraction) and the denominator (the bottom part of the fraction) separately. In this case, the numerator is 6, and the denominator is 7.
- Squaring the Numerator:
- The numerator, 6, when squared, becomes (6^2 = 36).
- Squaring the Denominator:
- The denominator, 7, when squared, becomes (7^2 = 49).
Putting these together gives us the fraction (\frac{36}{49}).
Additional Concepts
Squaring a fraction can be visualized in terms of area. If you have a square where each side is (\frac{6}{7}) units long, the area of that square is found by multiplying the length of one side by itself. Thus, the area (which is the square of the side length) will be ((\frac{6}{7})^2 = \frac{36}{49}).
Simplifying the Result
The fraction (\frac{36}{49}) is already in its simplest form because 36 and 49 have no common factors (36 is (6^2) and 49 is (7^2)). This means that the fraction cannot be reduced any further.
In summary, ((\frac{6}{7})^2) equals (\frac{36}{49}), derived by squaring both the numerator and the denominator.