Evaluate the Expression: (1/6)^5 Fraction Calculation

Insert the corresponding expression:

$\frac{1^5}{6^5}=$

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)

00:07 equals the numerator and denominator, raised to the same power (N)

00:14 We'll apply this formula to our exercise, only this time in the opposite direction

00:18 This is the solution

Step-by-Step Solution

To solve this problem, we need to express $\frac{1^5}{6^5}$ using the power of a fraction rule:

Step 1: Identify that both the numerator and denominator are raised to the same power, 5.
Step 2: Recognize that the expression can be rewritten as $\left(\frac{1}{6}\right)^5$ using the power of a fraction rule: $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$ .

Applying the formula, we convert $\frac{1^5}{6^5}$ into $\left(\frac{1}{6}\right)^5$ .

Therefore, the solution to the problem and correct multiple-choice answer is $\left(\frac{1}{6}\right)^5$ , which corresponds to choice 2.