Question

The half-life of helium-5 is 7.6 x 10^-22 seconds, and the half-life of helium-9 is 7 x 10^-21 seconds. Approximately how many times greater is the half-life of helium-9 than that of helium-5?

Answer 1

(7X10^-21)/(7.6X10^-22) is equal to:

(7/7.6)(10^-21/10^-22)

Rule for division of similar bases with exponents...

(a^b)/(a^c)=a^(b-c)

In this case we have (10^-21)/(10^-22)=10^(-21--22)=10^1

And 7/7.6≈0.921, and we only had two significant figures so 0.92 works

0.92X10^1

9.2

So the half life of helium-9 is about 9.2 times greater than the half life of helium-5