Explain how the quotient of powers was used to simplify this expression. 2 to the fifth power, over 8 = 22 by finding the quotient of the bases to be one fourth, and cancelling common factors by finding the quotient of the bases to be one fourth, and simplifying the expression by simplifying 8 to 23 to make both powers base two, and subtracting the exponents by simplifying 8 to 23 to make both powers base two, and adding the exponents

. If we change the 8 into a base of 2 raised to the 3rd power we can use the Quotient rule for exponents. Rewriting we have . The rule is that if the bases are the same (which they are) we can subtract the exponents, lower from upper. . So the reason we will choose is the third one: By simplifying 8 to to make both powers base 2, and subtracting the exponents.

step-by-step explanation:

the original amount doesn't ''re just looking for the time it takes for 1/2 of the substance to we have

(1/2) =)     take the ln   of both sides

ln (1/2)   = )   and we can write

ln(1/2) = ) lne     and lne   = 1     so we have

ln(1/2) = -.1092t     divide both sides by -.1092

t = ln(1/2)/-.1092 = about 6.347 days = about 6.3 days (rounded)

multiplication is multiplication.   it might feel harder depending on what level of math you are in, but generally it will be the same old stuff, while implementing some new concepts and methods of solving work.