Select all of the expressions that have a value between 0 an

Select all of the expressions that have a value between 0 and 1. A. 8^7 middot 8^-12 B. 7^4/7^-3 C. (1/3)^2 middot (1/3)^9 D. (-5)^6/(-5)^10 E. (-3)^0

Solution

A . 8⁷.8^-12 = 8^7-12 = 8^-5 = 1/8⁵ = 1/32768 ( as x^m.xⁿ = x^m+n and 1/x^m = x^-m)

B. 7⁴/7^-3 = 7⁴.7³ = 7⁴⁺³ = 7⁷ = 823543

C. (1/3)² .(1/3)⁹ =1/3²⁺⁹ = 1/3¹¹ = 1/177147 ( as 1^m =1)

D. (-5)⁶/(-5)¹⁰ = 1/[(-5)¹⁰(-5)^-6] = 1/(-5)^10-6 = 1/(-5)⁴ = 1/625

E. (-3)⁰ = 1 (as x⁰ =1)

The expressions that have a value between 0 and 1 are A, C and D ( In case of E,the expression equals 1)