Calculate (13/19)^7: Evaluating a Fraction Raised to the Seventh Power

To solve this problem, we'll follow these steps:

• Step 1: Identify the given expression $\left(\frac{13}{19}\right)^7$.
• Step 2: Apply the exponent rule for fractions: $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$.
• Step 3: Perform the calculation by raising both the numerator and the denominator to the power of 7.

Now, let's work through each step:
Step 1: The expression provided is $\left(\frac{13}{19}\right)^7$, which is a fraction raised to an exponent.
Step 2: Using the exponentiation rule for fractions: $\left(\frac{a}{b}\right)^n$ is equivalent to $\frac{a^n}{b^n}$.
Step 3: Applying this rule, we express $\left(\frac{13}{19}\right)^7$ as $\frac{13^7}{19^7}$.

Therefore, the solution to the problem is $\frac{13^7}{19^7}$, which corresponds to choice 1.