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Understanding Rational and Irrational Numbers in Exponential Equations

Learn about properties of rational and irrational numbers, solve exponential equations, and understand why adding or subtracting exponents makes sense. Determine whether the sum or product of numbers is rational or irrational. Explore patterns in results and the nature of irrational numbers.

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Understanding Rational and Irrational Numbers in Exponential Equations

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  1. Rational and Irrational Numbers and TheirProperties (1.1.2) September 6th, 2017

  2. Solving Exponential Equations

  3. Ex. 1: Simplify . Why does it make sense to add the exponents when multiplying variables of the same base?

  4. Ex. 2: Simplify . Why does it make sense to subtract the exponents when dividing variables of the same base?

  5. Ex. 3: Solve the equation .

  6. Ex. 4: Solve the equation .

  7. How can you determine whether the sum or product of two numbers will be rational or irrational?

  8. Ex. 1: Are the following sums and products rational or irrational? • a) b) • c) d) • e) f) • g) h)

  9. Do you see any pattern in what makes the result rational or irrational?

  10. Is the sum or product of two irrational numbers always irrational?

  11. Ex. 2: Are the following sums and products rational or irrational? • a) b) • c) d)

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