Which expressions are equivalent to 
 
 
 
 
\[\dfrac{1}{5}\cdot \dfrac{1}{5}\cdot \dfrac{1}{5}\cdot \dfrac{1}{5}\] 

To find expressions equivalent to 

\[
\dfrac{1}{5} \cdot \dfrac{1}{5} \cdot \dfrac{1}{5} \cdot \dfrac{1}{5}
\]

we can simplify by using the property of exponents for repeated multiplication of the same fraction.

### Step 1: Recognize the repeated multiplication
Since we have \(\dfrac{1}{5}\) multiplied by itself 4 times, we can write this as:
\[
\left(\dfrac{1}{5}\right)^4
\]

### Step 2: Evaluate the expression
To evaluate \(\left(\dfrac{1}{5}\right)^4\), calculate:
\[
\left(\dfrac{1}{5}\right)^4 = \dfrac{1^4}{5^4} = \dfrac{1}{625}
\]

### Equivalent Expressions
Thus, the following expressions are equivalent to the original:

1. \(\left(\dfrac{1}{5}\right)^4\)
2. \(\dfrac{1}{625}\)

Would you like more details on exponent rules, or do you have any other questions?

---

#### Related Questions:
1. How would you express \(\dfrac{1}{5} \cdot \dfrac{1}{5}\) with exponents?
2. What is the value of \(\left(\dfrac{1}{2}\right)^3\)?
3. How does the rule \((a^m)^n = a^{m \cdot n}\) apply to fractions?
4. If \(\dfrac{1}{5}\) is multiplied by itself 6 times, what is the result?
5. How can you convert \(\left(\dfrac{1}{5}\right)^4\) to a decimal?

#### Tip:
When multiplying a fraction by itself repeatedly, rewrite it with an exponent for simplicity and clarity.

Which expressions are equivalent to \[\dfrac{1}{5} \cdot \dfrac{1}{5} \cdot \dfrac{1}{5} \cdot \dfrac{1}{5}\]?

Explore how to find expressions equivalent to (1/5) multiplied by itself four times. This problem demonstrates the use of exponents with fractions, simplifying repeated multiplication. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation