Roots + Exponents

Question 1

Is result larger or smaller when base is greater than 1 and exponent is an even positive integer

Answer 1

Result is larger (e.g. 4^2=16)

Question 2

Is result larger or smaller when base is greater than 1 and exponent is an odd positive integer greater than 1

Answer 2

Result is larger (e.g. 4^3=64)

Question 3

Is result larger or smaller when base is less than -1 and exponent is an even positive integer

Answer 3

Result is larger (e.g. (-4)^2=16)

Question 4

Is result larger or smaller when base is less than -1 and exponent is an odd positive integer greater than 1

Answer 4

Result is smaller (e.g. (-4)^3=-64)

Question 5

Is result larger or smaller when base is a positive proper fraction and exponent is an even positive integer

Answer 5

Result is smaller (e.g. (1/4)^2=1/16

Question 6

Is result larger or smaller when base is a negative proper fraction and exponent is an even positive integer

Answer 6

Result is larger (e.g. (-1/4)^2=1/16)

Question 7

Is result larger or smaller when base is a positive proper fraction and exponent is an odd positive integer

Answer 7

Result is smaller; (1/4)^3=1/64

Question 8

Is result larger or smaller when base is a negative proper fraction and exponent is an odd positive integer

Answer 8

Result is larger; (-1/4)^3 = - 1/64

Question 9

0 to any power

Answer 9

0

Question 10

Is result larger or smaller when base is greater than 1 and exponent is a positive proper fraction

Answer 10

Result is smaller; 4^(1/2)=sqrt(4)

Question 11

Is result larger or smaller when base is a proper positive fraction and exponent is a positive proper fraction

Answer 11

Result is larger; (1/4)^(1/2) = sqrt(1/4) = 1/2

Question 12

If x is a proper positive fraction is x^2 or sqrt(x) larger?

Answer 12

sqrt(x) because if 0<x<1, then x^2<x<sqrt(x)

Question 13

sqrt(3)

Answer 13

~1.7

Question 14

sqrt(2)

Answer 14

~1.4

Question 15

sqrt(6)

Answer 15

~2.4

Question 16

sqrt(5)

Answer 16

~2.2

Question 17

sqrt(7)

Answer 17

~2.6

Question 18

sqrt(8)

Answer 18

~2.8