Question

Mr Rodriguez has owned his truck 3 months. in that time he has driven the truck a total of 4⁵ miles how many miles has he driven in 3 months

Answer 1

A number to the fifth power means to multiply that number 5 times by itself. In this case:

`4^5=4\cdot4\cdot4\cdot4\cdot4`

And now we can solve:

`4\cdot4\cdot4\cdot4\cdot4=16\cdot16\cdot4=16\cdot64`

Now we can factor out 2 of each one:

`16\cdot64=2\cdot2(8\cdot32)`

Then again:

`2(8\cdot32)=2\cdot2(2\cdot2(4\cdot16))`

Now we can solve the paretheses:

`2(2(4\cdot16)=2\cdot2(2\cdot2\cdot64)`

Finally, this are all multiplications of a number by 2, the we can solve it easily:

`2\cdot2(2\cdot2\cdot64)=2\cdot2(2\cdot128)=2\cdot2\cdot256=2\cdot512=1024`

The amount of miles driven in 3 months is 1024miles