3. Rational Exponents

4. Use the rules for combining fractions when the exponents are rational numbers X 2 3 X 1 2 (()) = X 2 3 + 1 2 = X 4 6 + 3 6 = X 7 6

5. 27 2 3 4 5 () = 2 3 X 4 5 = 8 15 Power of Powers …

6. The Exponent Laws will also allow for equations to be solved where variables are found in the exponents.

7. Solve for x: 1)2 x = 2 3 Because the bases are the same, we can equate the exponents and solve! x = 3

8. 2)2 6 = 4 x + 2 We can not use the exponents laws because……. Find a common base 4 = 2 2, therefore 2 6 = 2 2(x + 2) = 2 2x + 4 (equate exponents)

9. 6 = 2x + 4 -4 2 = 2x 1 = x Check the answer: 2 6 = 4 1 + 2 64 = 64

10. 3) 2 x - 1 = 8 Find a common base 8 = 2 3, therefore 2 x – 1 = 2 3 same base….. x – 1 = 3 x = 4

11. 4) 4 x + 2 = 16 Find a common base 4 = 2 2, 16 = 2 4, therefore 2 2(x + 2) = 2 4 same base….. 2(x + 2) = 4 2x + 4 = 4

12. 2x = 0 X = 0