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

00:00 Convert to power

00:04 Any number (M) multiplied by itself is actually squared

00:14 The number of times a number is multiplied by itself is the exponent

00:18 Let's count the number of times in our question

00:23 This is our exponent

00:33 Any fraction (A divided by B) to the power of (N)

00:36 Raises both numerator and denominator to the power of N

00:40 We'll use this formula in our exercise

00:45 1 to the power of any number (N) is always equal to 1

00:48 And this is the solution to the question

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