The expression shown in the image is:

$\left( \sqrt[5]{k} \right) (k)^{10}$

To simplify this expression, let's rewrite the terms with exponents.

1. $\sqrt[5]{k}$ can be expressed as $k^{\frac{1}{5}}$.
2. So, the expression becomes: $k^{\frac{1}{5}} \cdot k^{10}$

When multiplying terms with the same base, we add the exponents:

$k^{\frac{1}{5} + 10}$

Converting $10$ to a fraction gives us:

$k^{\frac{1}{5} + \frac{50}{5}} = k^{\frac{51}{5}}$

Thus, the simplified form of the expression is:

$k^{\frac{51}{5}}$

Would you like further details or have any questions?

Here are some related questions to explore:

1. How would the answer change if the exponent on $k$ were different, such as $k^8$ instead of $k^{10}$?
2. What happens if you change the root from a fifth root to a different root, like a square root?
3. How can you simplify expressions with different fractional exponents?
4. What is the general rule for multiplying terms with fractional exponents?
5. How would you handle an expression with a nested exponent, such as $(\sqrt[5]{k})^3$?

Tip: When working with exponents, remember that multiplying terms with the same base means adding the exponents, while dividing terms with the same base means subtracting the exponents.