1. if the product of the integers a, b, and c is 1, then what is the difference between the largest and the smallest possible values of a^2*b^3*c^4?
a. -2 b. -1 c. 1 d. 2

2. hats are purchased at the rate of $33 per dozen. if they are sold at a closeout sale for $2.50 each, the percent loss on the cost price is:
a. 3 b. 3 1/3 c. 9 1/11 d. 10

Problem 1

The largest value would be 1 and the smallest would be -1.

To get a product of 1, either all are 1 or two of the variables are -1 and the other one is 1.

Largest value = (1)^2 * (1)^3 * (1)^4 =1

Smallest value = (- 1)^2 * (- 1)^3 * (1)^4 = -1

The difference is:

largest value – smallest value = 1 – (-1) = 2

Therefore the answer is letter D.

Problem 2

% loss = (final price – initial price) * 100%/ initial price

where, final price per dozen = ( $2.50 / piece) (12 piece / dozen) = $30

Therefore,

% loss = ($30 - $33) * 100 / $33

% loss = - 300/ 33 = 9 1/11

Therefore the answer is letter C.

answer: 40.95

step-by-step explanation:

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.