Let's break down and solve the expression \(\frac{(\sqrt{7})^3}{7}\).

1. First, simplify \((\sqrt{7})^3\). The square root of 7 raised to the third power is:
   \[
   (\sqrt{7})^3 = 7^{3/2} = 7 \times \sqrt{7}
   \]
   
2. Now, divide this by 7:
   \[
   \frac{7 \times \sqrt{7}}{7}
   \]

3. The 7's cancel out, leaving:
   \[
   \sqrt{7}
   \]

Thus, the simplified result is \(\sqrt{7}\).

Would you like further clarification or more details?

Here are 5 related questions to expand your understanding:
1. How do you simplify expressions with square roots and exponents?
2. What are the properties of exponents when dealing with square roots?
3. How do you simplify expressions like \(\frac{a^m}{a^n}\)?
4. What is the relationship between powers and roots in algebraic expressions?
5. How would this expression change if it were \(\frac{(\sqrt{7})^4}{7}\)?

**Tip:** When working with square roots and exponents, remember that \(\sqrt{x} = x^{1/2}\), which helps simplify expressions efficiently.

Learn how to simplify the expression (√7)^3 / 7 step-by-step using exponentiation and square root rules. This algebraic problem focuses on simplifying expressions with exponents and roots, ideal for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation