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

explanation:

previous steps have made pa≅ pb ≅ st ≅ su. setting the compass width to ab allows you to make tu the same length. then δstu ≅ δpab by the sss congruence postulate, and ∠p ≅ ∠s by the reason cpctc.

45.36 feet per second.

step-by-step explanation:

to find the most accurate determination for the number of feet per second tyrone traveled on his way to work let us convert miles to feet and minutes to seconds.

1 mile = 5280 feet.

1 minute = 60 seconds.

now we will divide 158400 by 3492 to find the most accurate determination for the number of feet per second tyrone traveled on his way to work.

therefore, tyrone traveled on his way to work at the rate of 45.36 feet per second.