Simplity
- (sqrt(3 * 5 ^ - 3)) / [(sqrt(3 ^ - 1)) * sqrt(5) ]* 6root(3 * 5 ^ 4, 5)

Let's simplify the following expression:

\[
\frac{\sqrt{3 \cdot 5^{-3}}}{\sqrt{3^{-1}} \cdot \sqrt{5}} \cdot \sqrt[6]{\frac{3 \cdot 5^4}{5}}
\]

We will approach this step by step.

### Step 1: Simplifying the Numerator

The numerator is:

\[
\sqrt{3 \cdot 5^{-3}}
\]

Since square root distributes over multiplication:

\[
\sqrt{3 \cdot 5^{-3}} = \sqrt{3} \cdot \sqrt{5^{-3}} = \sqrt{3

Simplify (sqrt(3 * 5^-3)) / [(sqrt(3^-1)) * sqrt(5)] * 6root(3 * 5^4, 5)

Learn how to simplify the expression (sqrt(3 * 5^-3)) / [(sqrt(3^-1)) * sqrt(5)] * 6th root of (3 * 5^4, 5). This problem explores key algebraic concepts involving exponents, radicals, and root functions. Suitable for students in Grades 10-12.

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