Evaluate (5/y)^7: Simplifying a Fraction Raised to the 7th Power

Insert the corresponding expression:

$\left(\frac{5}{y}\right)^7=$

To solve this problem and transform the expression $\left(\frac{5}{y}\right)^7$, we need to utilize the exponent rule for powers of fractions:

• Step 1: Recognize that the expression $\left(\frac{5}{y}\right)^7$ involves both the numerator 5 and the denominator $y$.
• Step 2: According to the exponent rule $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$, we can apply the exponent of 7 to both the numerator and the denominator.
• Step 3: Applying this rule gives us $\frac{5^7}{y^7}$. This step distributes the power to each component of the fraction, preserving the structure of the expression.

Thus, the simplified form of the expression $\left(\frac{5}{y}\right)^7$ is $\frac{5^7}{y^7}$.

This matches choice 3 from the provided options.