Simplify the Quartic Fraction: x⁴/a⁴ Expression Problem

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

• Step 1: Identify the given information: We have the expression $\frac{x^4}{a^4}$.
• Step 2: Apply the appropriate exponent rule: Use the rule $\frac{x^m}{y^m} = \left(\frac{x}{y}\right)^m$.
• Step 3: Simplify the expression using the rule: Substitute $m$ with 4, $x$ with $x$, and $y$ with $a$.

Now, let's work through each step:
Step 1: The expression is $\frac{x^4}{a^4}$.
Step 2: We use the rule $\frac{x^m}{y^m} = \left(\frac{x}{y}\right)^m$, which states that a fraction where the numerator and denominator are raised to the same power can be expressed as a power of a single fraction.
Step 3: Plugging in the values, we have $\frac{x^4}{a^4} = \left(\frac{x}{a}\right)^4$.

Therefore, the solution to the problem is $\left(\frac{x}{a}\right)^4$, which corresponds to choice 1.