Exponential equations not requiring logarithms solve show work 5^w * 5^-3w = 1/125 and 8^b-1 * 8^4b = 8^3b

5^w * 5^-3w = 1/125

when the base is the same we add the exponents

a faction is a negative exponent

5^(w-3w) = 125^-1  

a power to a power is multiplied

5^-2w = (5^3)^-1

5^-2w = 5^ -3

since the bases are the same the exponents are equal

-2w = -3

divide by -2

w = 3/2

8^b-1 * 8^4b = 8^3b

since the bases are the same add the exponents

8^(b-1+4b) = 8^3b

8^(5b-1) = 8^3b

since the bases are the same the exponents must be the same

5b-1 = 3b

subtract 5b from each side

-1 = -2b

divide by -2

1/2 =b

q1 a person or thing situated away or detached from the main body or system. a cluster is a a mash of many things.

q2 do

step-by-step explanation:

answer: i don't understand it

step-by-step explanation: sorry