5. (root(160, 5))/(root(5, 5))

6. root(32 ^ 4, 5)

Let's solve the given expressions one by one.

### Expression 5: 
\[
\frac{\sqrt[5]{160}}{\sqrt[5]{5}}
\]

Using the property of radicals that says \(\frac{\sqrt[n]{a}}{\sqrt[n]{b}} = \sqrt[n]{\frac{a}{b}}\), we can simplify this:

\[
\frac{\sqrt[5]{160}}{\sqrt[5]{5}} = \sqrt[5]{\frac{160}{5}} = \sqrt[5]{32}
\]

Since \(32 = 2^5\), we know that:

\[
\sqrt[5]{32} = 2
\]

So, the value of the expression is:

\[
2
\]

### Expression 6:
\[
\sqrt[5]{32^4}
\]

We know that \(32 = 2^5\), so:

\[
32^4 = (2^5)^4 = 2^{20}
\]

Now, applying the 5th root to \(2^{20}\):

\[
\sqrt[5

5. (root(160, 5))/(root(5, 5))
6. root(32 ^ 4, 5)

Learn how to simplify the radical expressions (root(160, 5))/(root(5, 5)) and root(32^4, 5) using properties of radicals and exponents. This step-by-step solution is designed for high school students, covering key concepts such as radical simplification and exponent rules.

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