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

Question

asked Dec 25, 2023 45.8k views

1 Answer

Rick Mogstad · Answer 1 · 2023-12-29T22:03:05+0000

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