Solve (13×21)/(11×10) Raised to the 6th Power: Complex Fraction Expression

To solve this problem, we need to simplify the expression $\left(\frac{13 \times 21}{11 \times 10}\right)^6$ by correctly distributing the exponent of 6 throughout both the numerator and the denominator.

Step 1: Start by applying the exponent of 6 to the entire fraction using the property $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$. This means that each component of the numerator and the denominator will be raised to the power of 6 separately.

Step 2: Apply the exponent to the numerator: $(13 \times 21)^6 = 13^6 \times 21^6$.

Step 3: Similarly, apply the exponent to the denominator: $(11 \times 10)^6 = 11^6 \times 10^6$.

Step 4: Combine these results, noting that each term now has the exponent applied: $\left(\frac{13 \times 21}{11 \times 10}\right)^6 = \frac{13^6 \times 21^6}{11^6 \times 10^6}$.

Thus, the solution to the expression, when simplified, is $\frac{13^6 \times 21^6}{11^6 \times 10^6}$, which corresponds to choice 1.