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Fractional Exponents and Radicals

Fractional Exponents and Radicals. Fractional Exponents: Calculator Warning. Calculate the following in your calculator:. Not Exact. What is the exact value of 2 1/2 ?. 2 ^ ( 1 ÷ 2 ) . A Math Trick to Evaluate 2 ½ Exactly. Evaluate the following using Exponential Laws:

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Fractional Exponents and Radicals

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  1. Fractional Exponents and Radicals

  2. Fractional Exponents: Calculator Warning Calculate the following in your calculator: Not Exact. What is the exact value of 21/2? 2 ^ ( 1 ÷ 2 )

  3. A Math Trick to Evaluate 2½ Exactly Evaluate the following using Exponential Laws: 21/2.21/2 When multiplying, if the bases are the same add the exponents 21/2+ 1/2 = 21 Now use this result to figure out what 21/2 equals. 2

  4. What Does 2½ Exactly Equal? Since: The final answer makes sense because: What is the number whose square is 2: x2 = 2 ?

  5. Irrational Numbers Radical numbers/Fractional Roots are typically irrational numbers (unless they simplify to an integer). Our calculator gives: But the decimal will go on forever because it is an irrational number. For the exact answer just use:

  6. More Fractional Exponents Change the following into a radical: 21/3= Remember 21/2 is also called the square root of 2 The cube root of 2. The solution to x3 = 2

  7. nth Roots The nth root of a number x is a number r which, when multiplied by itselfn times equalsx. Examples:

  8. Radical v. Exponential Notation Rewrite the following roots as an exponential expression:

  9. Square Root Notation Remember: The 2 is implied!

  10. Roots in the Calculator Exponential Notation: 1 2 ^ ( 1 ÷ 6 ) Radical Notation: ( 6 ) ( 1 2 ) MATH is found in #5

  11. Fractional Exponents with Numerators greater than 1 Approximate the following expression: 25/3≈ Find the exact value: Expand Rewrite in Radical Notation Simplify

  12. Exponential v. Radical Notation bp/q= Generally b≥0

  13. Example Evaluate the following without a calculator: Rewrite in Radical Notation Simplify By rewriting the fractional exponential expression into a radical expression, the arithmetic is more straightforward.

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