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tell the answer only for a and others how to do it not answer

For part **a**:

\( 10^{2/3} \) can be rewritten in two ways:
1. \( \sqrt[3]{10^2} \)
2. \( (\sqrt[3]{10})^2 \)

For the other parts, here is how to approach them:

**b. \( (\sqrt[4]{9})^4 \)**  
To rewrite this, you can think of converting it to fractional exponents or rewriting it as a root raised to a power.

**c. \( 5 \sqrt{x^3} \)**  
Express the square root and cube using fractional exponents and try to simplify.

**d. \( (\sqrt{2})^5 \)**  
Consider converting the square root into an exponent form and then simplify.

**e. \( 5^{7/2} \)**  
Think about expressing this as a square root or raising the base to a power.

**f. \( y^{3/3} \)**  
Simplify the fractional exponent or rewrite it to get an equivalent integer expression.

Would you like further details or have any questions? 

Here are 5 related questions to practice:
1. How would you rewrite \( 8^{4/3} \) in two different ways?
2. Can \( 27^{2/3} \) be expressed as a root? If so, how?
3. What is another way to express \( 5^{1/2} \)?
4. Simplify \( (x^{1/4})^4 \).
5. Write \( 16^{3/4} \) using radical notation.

**Tip:** When dealing with fractional exponents, remember that \( a^{m/n} \) can be seen as the \( n \)-th root of \( a^m \) or \( (a^{1/n})^m \).

Rewrite the given expressions involving roots and fractional exponents in two different ways, such as for 10^(2/3) in part a.

Learn how to rewrite expressions involving roots and fractional exponents, including examples like 10^(2/3), (sqrt[4]{9})^4, and (sqrt{2})^5. Suitable for high school algebra students.

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