Why is it important to check all solutions to radical equations?

What is the pattern in the values as the exponents increase?

Ariana starts with 100 milligrams of a radioactive substance. the amount of the substance decreases by 20% each week for a number of weeks, w. the expression 100(1−0.2)w finds the amount of radioactive substance remaining after w weeks. which statement about this expression is true? a) it is the difference between the initial amount and the percent decrease. b) it is the difference between the initial amount and the decay factor after w weeks. c) it is the initial amount raised to the decay factor after w weeks. d) it is the product of the initial amount and the decay factor after w weeks.

Money off coupons have been circulated to 300 households. only 2/5 of these were redeemed (used) in the local supermarket to get a free shampoo. what fraction of coupons were unused? (ps: write how you got the answer)