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Writing Radicals in Rational Form

Writing Radicals in Rational Form. Section 10.2. DEFINITIONS. Base: The term/variable of which is being raised upon Exponent: The term/variable is raised by a term. AKA Power. EXPONENT. BASE. THE EXPONENT. NTH ROOT RULE. M is the power (exponent) N is the root A is the base.

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Writing Radicals in Rational Form

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  1. Writing Radicals in Rational Form Section 10.2 10.2 - Rational Exponents

  2. DEFINITIONS Base: The term/variable of which is being raised upon Exponent: The term/variable is raised by a term. AKA Power EXPONENT BASE 10.2 - Rational Exponents

  3. THE EXPONENT 10.2 - Rational Exponents

  4. NTH ROOT RULE • M is the power (exponent) • N is the root • A is the base 10.2 - Rational Exponents

  5. RULES Another way of writing is 251/2. is written in radical expression form. 251/2 is written in rational exponent form. Why is square root of 25 equals out of 25 raised to ½ power? 10.2 - Rational Exponents

  6. EXAMPLE 1 Evaluate 43/2 in radical form and simplify. 10.2 - Rational Exponents

  7. EXAMPLE 1 Evaluate 43/2in radical form and simplify. 10.2 - Rational Exponents

  8. EXAMPLE 2 Evaluate 41/2 in radical form and simplify. 10.2 - Rational Exponents

  9. YOUR TURN Evaluate (–27)2/3 in radical form and simplify. 10.2 - Rational Exponents

  10. EXAMPLE 3 Evaluate –274/3 in radical form and simplify. Use calculator to check Hint: Remember, the negative is OUTSIDE of the base 10.2 - Rational Exponents

  11. EXAMPLE 4 Evaluate in radical form and simplify. 10.2 - Rational Exponents

  12. NTH ROOT RULE • M is the power (exponent) • N is the root • A is the base DROP AND SWAP 10.2 - Rational Exponents

  13. EXAMPLE 5 Evaluate (27)–2/3 in radical form and simplify. 10.2 - Rational Exponents

  14. EXAMPLE 6 Evaluate (–64)–2/3 in radical form and simplify. 10.2 - Rational Exponents

  15. YOUR TURN Evaluate in radical form and simplify. 10.2 - Rational Exponents

  16. PROPERTIES OF EXPONENTS Product of a Power: Power of a Power: Power of a Product: Negative Power Property: Quotient Power Property: 10.2 - Rational Exponents

  17. EXAMPLE 7 Simplify • Saying goes:BASE, BASE, ADD If the BASES are the same, ADD the powers 10.2 - Rational Exponents

  18. EXAMPLE 8 Simplify 10.2 - Rational Exponents

  19. YOUR TURN Simplify 10.2 - Rational Exponents

  20. EXAMPLE 9 Simplify • Saying goes:POWER, POWER, MULTIPLY If the POWERS are near each other, MULTIPLY the powers – usually deals with PARENTHESES 10.2 - Rational Exponents

  21. EXAMPLE 10 Simplify 10.2 - Rational Exponents

  22. YOUR TURN Simplify 10.2 - Rational Exponents

  23. EXAMPLE 11 Simplify • Saying goes:When dividing an expression with a power, SUBTRACT the powers. 10.2 - Rational Exponents

  24. EXAMPLE 12 Simplify 10.2 - Rational Exponents

  25. EXAMPLE 13 Simplify 10.2 - Rational Exponents

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