Simplify (b/5)⁴: Evaluating the Fourth Power of a Fraction

To solve this problem, we'll apply the exponent rule for fractions:

• Step 1: Identify the fraction $\frac{b}{5}$ and the power $4$.
• Step 2: Apply the exponent to both the numerator and the denominator, as per the formula.
• Step 3: Use the rule $\left(\frac{b}{5}\right)^4 = \frac{b^4}{5^4}$.

Now, let's work through the application:
Step 1: We have the base fraction $\frac{b}{5}$ and exponent $4$.
Step 2: According to the exponent rule, $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$, apply the exponent $4$ to both $b$ and $5$.
Step 3: This results in the expression $\frac{b^4}{5^4}$.

Therefore, the expression $\left(\frac{b}{5}\right)^4$ simplifies to $\frac{b^4}{5^4}$.