Assess Readiness
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Look at Part 1. How can you simplify the expression
(x^2)^3 ? Explain.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). -
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How can you rewrite
\frac{x^{10}}{x^{15}} ?Answers vary; help students recall the quotient rule.
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Can
x^{-5} be simplified further? Why or why not?Yes; it has a negative exponent, which can be rewritten as a positive exponent in the denominator:
\frac{1}{x^5} . -
Look at Part 2. How many times do you need to multiply
2 by itself to get8? Three times.
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If you rewrite this expression using an exponent, what will the base be? What kind of exponent will there be?
5 will be the base; there will be a fractional exponent. -
What should the numerator of the exponent be? Why?
1 ; it is the power that5 is raised to in the radical. -
What should the denominator of the exponent be? Why?
3 ; it is the index of the radical. -
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