The expression you have is:

\[
\frac{1}{5^{-3}}
\]

We can rewrite this using the property of exponents, which states that \( a^{-n} = \frac{1}{a^n} \), and vice versa.

Thus:

\[
\frac{1}{5^{-3}} = 5^{3}
\]

Now, calculate \( 5^3 \):

\[
5^3 = 5 \times 5 \times 5 = 125
\]

So, the value of \( \frac{1}{5^{-3}} \) is:

\[
125
\]

Would you like further clarification or more details?

Here are 5 related questions for practice:
1. What is \( 5^{-2} \) in simplified form?
2. How would you simplify \( \frac{1}{2^{-4}} \)?
3. What is \( 7^{-3} \times 7^{4} \)?
4. How do you simplify \( \left( \frac{1}{5} \right)^{-2} \)?
5. What is \( 6^{0} \) and why?

**Tip:** When you have a negative exponent, flip the base to the reciprocal and make the exponent positive.

Learn how to simplify the expression 'one over 5 to the negative 3' using exponent rules. This guide covers the key concepts of negative exponents and reciprocals, providing a clear step-by-step solution. Ideal 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