Powers and Roots

Question 1

Exponent Laws

Answer 1

(x^a)(x^b) = x^(a + b); (x^a)/(x^b) = x^(a - b) = 1/(x^b-a); (x^a)^b = x^(ab); (x^a)(y^a) = (xy)^a; (x/y)^a = x^a/y^a

Question 2

1 and 0 as bases

Answer 2

1^a=1. 0^a=0. a^0=1. 0^0 is undefined.

Question 3

Negative exponents

Answer 3

x^(-a) = 1/(x^a); Ex. x^(-2) = 1/(x^2)

Question 4

Fractions as exponents

Answer 4

x^(1/2) = √x ; x^(2/3) = cube√(x^2)

Question 5

Negative bases

Answer 5

A negative # raised to an even power is +; raised to an odd power is -; NOTE: without ( ) means exponent is applied before - sign ex. -3^2 = -9

Question 6

Square roots of negative numbers

Answer 6

They have no real solutions, not defined in real # system

Question 7

10 as the base

Answer 7

To raise 10 to any power, just put that many 0s after the 1. 10^5 = 100,000 a 1 with 5 zeros.

Question 8

Perfect squares

Answer 8

Numbers with integers as their square roots: 4, 9, 16, etc; To estimate square roots of numbers that aren’t perfect squares, just examine the nearby perfect squares. Ex. find √50, know that √49 = 7 and √64 = 8, so √50 is btwn 7 and 8.

Question 9

Simplifying roots

Answer 9

Separate the number into its prime factors, and take out matching pairs Ex. √54 = √(9 x 6) = √9 x √6 = 3√6

Question 10

Adding roots

Answer 10

Can be added like variables Ex. 2√7 + 9√7 = 11√7

Question 11

General Rules for Roots

Answer 11

(√a)^2 = a ; √(a^2) = a ; (√a)(√b) = √ab ; (√a)/(√b) = √(a/b)