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

Insert the corresponding expression:

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

Video Solution

Solution Steps

00:00 Simplify the following problem

00:03 According to the laws of exponents, a fraction raised to a power (N)

00:08 equals the numerator and denominator raised to the same power (N)

00:11 We will apply this formula to our exercise

00:14 We'll raise both the numerator and the denominator to the power (N)

00:17 This is the solution

Step-by-Step Solution

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.