1. Look at Part 1. How can you simplify the expression (x^2)^3​? Explain.

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   x^6. You can rewrite the term as (x^2)^3=x^2\cdot x^2\cdot x^2 =x\cdot x \cdot x \cdot x\cdot x\cdot x=x^6​ (more generally, when you raise a power to a power, you multiply the exponents).

2. What is x^6\cdot x^4​​ in simplest form?

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   x^{10}

3. How can you rewrite \frac{x^{10}}{x^{15}}​​?

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   Answers vary; help students recall the quotient rule.
   

4. Rewrite \frac{x^{10}}{x^{15}} as a single exponential term.

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   x^{-5}

5. Can x^{-5}​ be simplified further? Why or why not?

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   Yes; it has a negative exponent, which can be rewritten as a positive exponent in the denominator: \frac{1}{x^5}.
   

6. Look at Part 2. How many times do you need to multiply 2 by itself to get 8?​

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   Three times.

7. How can you rewrite 8 as a power of 2?

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   2^3

8. Look at Part 3. What is the radicand of the expression?

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   5

9. If you rewrite this expression using an exponent, what will the base be? What kind of exponent will there be?

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   5​ will be the base; there will be a fractional exponent.
   

10. What should the numerator of the exponent be? Why?

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    1; it is the power that 5 is raised to in the radical.
    

11. What should the denominator of the exponent be? Why?

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    3; it is the index of the radical.
    

12. So, what is the equivalent exponential expression?

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    5^{\frac{1}{3}}

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