Evaluate (2×6)/(5×7) Raised to the Fourth Power: Fraction Expression

To solve this problem, we will simplify the expression $\left(\frac{2 \times 6}{5 \times 7}\right)^4$.

• Step 1: Apply exponent rules to the expression:
  Since $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$, we have: $\left(\frac{2 \times 6}{5 \times 7}\right)^4 = \frac{\left(2 \times 6\right)^4}{\left(5 \times 7\right)^4}$
• Step 2: Further break down $\left(2 \times 6\right)^4$ and $\left(5 \times 7\right)^4$ using $(ab)^n = a^n \times b^n$:
  $\left(2 \times 6\right)^4 = 2^4 \times 6^4$ $\left(5 \times 7\right)^4 = 5^4 \times 7^4$
• Step 3: Substitute back to see if match with any choices:
  $\frac{\left(2 \times 6\right)^4}{\left(5 \times 7\right)^4} = \frac{2^4 \times 6^4}{5^4 \times 7^4}$
• Step 4: Compare results with choices:
  Both $\frac{\left(2 \times 6\right)^4}{\left(5 \times 7\right)^4}$ and $\frac{2^4 \times 6^4}{5^4 \times 7^4}$ are forms of the same answer, indicating they are all correct simplifications.

Hence, according to the choices provided, all answers are correct.