Simplify the Expression: (1/5) Multiplied Four Times

Which of the following represents the expression below?

$\frac{1}{5}\cdot\frac{1}{5}\cdot\frac{1}{5}\cdot\frac{1}{5}$ ?

Video Solution

Solution Steps

00:08 First, let's convert to power.

00:12 Remember, when a number, M, is multiplied by itself, it's squared.

00:22 The exponent tells us how many times a number is multiplied by itself.

00:27 Now, let's count the repetitions in our question.

00:31 This gives us our exponent!

00:41 For a fraction, A divided by B, raised to N,

00:45 we raise both the numerator and denominator to the power of N.

00:50 Let's apply this rule to our exercise.

00:54 One to the power of any number, N, is always one.

00:58 And that's how we solve this problem!

Step-by-Step Solution

To solve the problem, let's represent the repeated multiplication using exponents:

We start with the given expression:

$\frac{1}{5} \cdot \frac{1}{5} \cdot \frac{1}{5} \cdot \frac{1}{5}$

Notice that $\frac{1}{5}$ is multiplied by itself four times. This can be expressed as a power:

$(\frac{1}{5})^4$

Hence, the correct representation of the given expression is $(\frac{1}{5})^4$ .

From the given choices, the correct option is Choice 4: $(\frac{1}{5})^4$ .

Therefore, the solution to the problem is $(\frac{1}{5})^4$ .