The question asks to rewrite the given expression using exponential notation.

Expression provided:

$\sqrt[7]{x y^{35} z^2}$

Step-by-step conversion:

1. Convert the root: The seventh root can be written as a fractional exponent of $\frac{1}{7}$. This means: $\sqrt[7]{A} = A^{\frac{1}{7}}$

2. Apply the fractional exponent to each term: $\sqrt[7]{x y^{35} z^2} = (x y^{35} z^2)^{\frac{1}{7}}$

   Distribute $\frac{1}{7}$ across all terms inside the parentheses: $x^{\frac{1}{7}} \cdot (y^{35})^{\frac{1}{7}} \cdot (z^2)^{\frac{1}{7}}$

3. Simplify exponents:

   • $y^{35 \cdot \frac{1}{7}} = y^5$
   • $z^{2 \cdot \frac{1}{7}} = z^{\frac{2}{7}}$

   Therefore: $x^{\frac{1}{7}} \cdot y^5 \cdot z^{\frac{2}{7}}$

Final Answer:

$x^{\frac{1}{7}} y^5 z^{\frac{2}{7}}$

Would you like me to provide additional details or examples? Here are five related questions for practice:

1. How do you express the cube root of $a^6 b^9$ using exponential notation?
2. Rewrite $\sqrt[4]{m^8 n^2}$ in exponential form.
3. How can you simplify $(x^5)^{\frac{1}{3}}$?
4. What is the general rule for applying fractional exponents to products inside parentheses?
5. Can you convert $16^{3/4}$ into radical notation?

Tip:

Remember that fractional exponents represent roots! For example, $a^{m/n}$ means $\sqrt[n]{a^m}$.