Simplity

- (sqrt(3 * 5 ^ - 3)) / (sqrt(3 ^ - 1)) * sqrt(5) * root(3 * 5 ^ 4, 5)

Let's simplify the given expression:

\[
\frac{\sqrt{3 \cdot 5^{-3}}}{\sqrt{3^{-1}}} \times \sqrt{5} \times \sqrt[5]{3 \cdot 5^4}
\]

### Step-by-step simplification:

1. **Simplify the square roots**:
   - \(\sqrt{3 \cdot 5^{-3}}\) can be written as \(\sqrt{3} \times \sqrt{5^{-3}} = \sqrt{3} \times 5^{-\frac{3}{2}}\).
   - \(\sqrt{3^{-1}} = 3^{-\frac{1}{2}}\).

   So the first part of the expression becomes:

   \[
   \frac{\sqrt{3} \times 5^{-\frac{3}{2}}}{3^{-\frac{1}{2}}}
   \]

2. **Simplify this fraction**:
   Using the properties of exponents:

   \[
   \frac{\sqrt{3}}{3^{-\frac{1}{2}}} = 3^{\frac{1}{2} + \frac{1}{2}} = 3^1 = 3
   \]

   So the expression simplifies to:

   \[
   3 \times 5^{-\frac{3}{2}}
   \]

3. **Include the rest of the expression**:
   Now include the rest of the terms: \(\sqrt{5} \times \sqrt[5]{3 \cdot 5^4}\).

   Let's simplify \(\sqrt[5]{3 \cdot 5^4}\):
   - \(\sqrt[5]{

(sqrt(3 * 5 ^ - 3)) / (sqrt(3 ^ - 1)) * sqrt(5) * root(3 * 5 ^ 4, 5)

Simplify the mathematical expression (sqrt(3 * 5 ^ -3)) / (sqrt(3 ^ -1)) * sqrt(5) * root(3 * 5 ^ 4, 5) using exponent rules and properties of radicals. This solution demonstrates step-by-step simplification, focusing on key concepts like exponents, square roots, and radicals. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation