7.1 nth roots and rational Exponents

Nth root rules Given 𝑛 𝑎 where n is the root and a is positive or negative number .( 𝑛 𝑎 = 𝑎 1 𝑛 ) If n is an odd root , the expression has one answer. If n is an even root, the expression can have two or zero real roots. ( no imaginary for now)

Examples of nth roots Simplify 1. Find the 3rd root of -64 2. Find the 2nd root of -100 3. Find the 5rd root of 32 4. Find the 4rd root of 81

Write in exponent notation or radical notation. 5. 6 𝑥 =______ 6. 𝑚 78 =______ 7. 𝑛 1 33 = ____ 8. 76 1 𝑦 = ____

Evaluate with no calculator. 9. 25 1 2 = ____ 10. 32 1 5 = ____ 11. 9 3 2 = ____ 12. 16 3 4 = ____

Evaluate with calculator. 13. 63 1 7 = ____ 14. 441 6 5 = ____ 15. 12 3 2 = ____ 16. 82 3 4 = ____

Solving Equations 17. 𝑥 3 −35=−100 18. 𝑥 4 −6=−22 19. 76−𝑥 7 =−31 17. 𝑥 3 −35=−100 18. 𝑥 4 −6=−22 19. 76−𝑥 7 =−31 20. 𝑥 6 −33=213

H.W. pg #404-405 #13-61 all