express \sqrt[7]{x^{35}} as a power of a power then simplify

To express \( \sqrt[7]{x^{35}} \) as a power of a power, follow these steps:

1. Rewrite the radical as a fractional exponent:
   \[
   \sqrt[7]{x^{35}} = x^{35/7}
   \]

2. Simplify the fraction \( 35/7 \):
   \[
   x^{35/7} = x^5
   \]

Thus, \( \sqrt[7]{x^{35}} = x^5 \).

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Here are 5 related questions for practice:
1. Express \( \sqrt[5]{x^{20}} \) as a power of a power, then simplify.
2. Simplify \( \sqrt[3]{x^9} \) as a power of \( x \).
3. Express \( \sqrt[4]{x^{12}} \) as a power of a power and simplify.
4. Simplify \( \sqrt[6]{x^{18}} \) and express it as a power of \( x \).
5. How would you express \( \sqrt[2]{x^{10}} \) in simplified form?

**Tip:** When simplifying radicals involving exponents, always remember that \( \sqrt[n]{x^m} = x^{m/n} \).

express \( \sqrt[7]{x^{35}} \) as a power of a power then simplify

Learn how to simplify the expression \( \sqrt[7]{x^{35}} \) by converting it to a fractional exponent and applying the laws of exponents. This step-by-step guide covers key algebraic concepts, including the fractional exponents rule. Suitable for students in Grades 9-11.

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