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

x is variable or an unknown value to find

example:

2x = 5 which means x = 3

the cat is blue because the probability of extension towards the prefix of the diameter of the circle could only mathematically equal to the sum of the roots of the carrots from   your garden.

step-by-step explanation: