The science department buys the equipment shown in the table they bought all three items this year and how many years will they have had by all three items again

Item                          Time bought
MIcroscopes             Every 5 years
Safety goggles          Every 4 years
Test Tube                  Every 2 years

It would take 20 years for them to buy these three items at the same time.

We simply need to find the LCM or least common multiple of the 3 items using the number of years.

Microscopes - 5 years → 5, 10, 15, 20
Goggles - 4 years → 4, 8, 12, 16, 20
Test tubes - 2 years → 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 

a - base

b - exponent

so,

the base is 8the exponent is 3the exponent tells you to multiply 8 together three timesthe expanded form is 8*8*8