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Simplifying and Evaluating Exponential Expressions and Nth Roots

Learn how to simplify, graph, and solve exponential expressions, equations, functions, and sequences. Explore writing and evaluating nth roots of numbers.

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Simplifying and Evaluating Exponential Expressions and Nth Roots

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  1. Do Now 1/17/19 • Copy HW in your planner. • Text p. 303, #4-34 evens • With your partner, complete Explorations 1 & 2 on page 173 in your Student Journal.

  2. Essential QuestionHow can you write and evaluate an nth root of a number? With your partner, complete Explorations 1 & 2 on page 173 in your Student Journal.

  3. Learning Target • Learning Goal • SWBAT simplify, graph, and solve exponential expressions, equations, functions and sequences. SWBAT evaluate expressions with rational exponents

  4. Section 6.2 “Radical and Rational Exponents” If bn = athen bis the nth root of a. radical index radicand Radical form Rational form

  5. If bn = athen bis the nth root of a. Radical form Rational form If 34 = 81then 3is the 4th root of 81. If 25 = 32then 2is the 5th root of 32.

  6. Finding nth Roots • If n is odd, then a has one real nthroot: • If n is even and a > 0, then a has 2 real nthroots: • If n is even and a = 0, then a has 1 real nthroot: • If n is even and a < 0, then a has 0 real nthroots.

  7. Find the indicated nth root of a. n = 3; a = -64 n = 4; a = 625 The index is odd, so 64 has one real root. Because (-4) x (-4) x (-4) is equal to -64, the cube root of -64 is -4. The index is even, so 625 has two real roots. Because 54 = 625 and (-5)4 = 625, the 4th roots of 625 are ±5.

  8. Try It OutFind the indicated nth root of a. n = 6; a = 64 n = 2; a = -16 The index is even, so 64 has two real roots. Because 26 = 64 and (-2)6 = 64, the 6th roots of 64 are ±2. The index is even, but the radicand (-16) is negative therefore, there are NO REAL ROOTS.

  9. Evaluating nth root expressions. Rewrite the expression showing factors. Then evaluate. Rewrite in radical form. Rewrite the expression showing factors. Then evaluate.

  10. Try It Out…Evaluating nth root expressions. The index is even, but the radicand (-81) is negative therefore, there are NO REAL ROOTS. Rewrite in radical form. Rewrite the expression showing factors. Then evaluate. Rewrite in radical form. Rewrite the expression showing factors. Then evaluate.

  11. Rational Exponents A rational exponent does not have to be of the form 1/n. Other rational numbers can also be used as exponents.

  12. Evaluating expressions with rational expressions.

  13. Try it out...

  14. Real-Life

  15. Homework • Text p. 303, #4-34 evens

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