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Rational Numbers as Exponents

Rational Numbers as Exponents. Simplify the following…are the answers the same or different? . Combination of Roots & Powers. For any nonnegative number a, any natural-number index k, and any integer m: You can raise to a power then take a root or vice versa. Examples. Try .

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Rational Numbers as Exponents

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  1. Rational Numbers as Exponents • Simplify the following…are the answers the same or different?

  2. Combination of Roots & Powers • For any nonnegative number a, any natural-number index k, and any integer m: • You can raise to a power then take a root or vice versa.

  3. Examples

  4. Try • Simplify and show another way to simplify

  5. Rational Exponents • For any nonnegative number a and any index k: • Example:

  6. Examples • Write without rational exponents • Write with rational exponents

  7. What if the exponent changes from 1/k? • Example:

  8. Negative Exponents

  9. Simplifying using Rational Exponents • Examples • Try

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