Calculate (6/8)² : Square of a Fraction Problem

To solve this problem, we'll compute $\left(\frac{6}{8}\right)^2$ using the rule for powers of a fraction:

• Step 1: Identify the numerator and denominator: $a = 6$ and $b = 8$.
• Step 2: Apply the formula $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$ with $n = 2$.
• Step 3: Calculate $a^n = 6^2$.
• Step 4: Calculate $b^n = 8^2$.

Now, let's carry out the calculations:

Step 3: $6^2 = 36$.

Step 4: $8^2 = 64$.

Therefore, $\left(\frac{6}{8}\right)^2 = \frac{36}{64}$.

We compare $\frac{36}{64}$ with the given answer choices:

• Choice 1: $\frac{12}{16}$ is not equal.
• Choice 2: $\frac{6}{64}$ is not equal.
• Choice 3: $\frac{36}{64}$ matches our result.
• Choice 4: $\frac{36}{8}$ is not equal.

Therefore, the correct answer is $\frac{36}{64}$, which matches Choice 3.