Can you solve 2¹⁸ − 1 without a calculator? Many people get stuck when they encounter large powers, but there's a clever way to approach this maths challenge!
In this video, you'll tackle an interesting exponent's problem that tests your mental maths, number skills and mathematical reasoning. Before watching the solution, take a moment to work it out yourself.
Your challenge:Find the value of 2¹⁸ − 1 without using a calculator.
Watch until the end to discover the solution and learn how to approach similar maths problems more efficiently.
If you enjoy maths tricks, mental maths challenges, powers and exponents, mathematical puzzles, and problem-solving techniques, subscribe for more engaging maths lessons and challenges.
Comment below: Did you solve it before seeing the answer?
Hello, this is a challenge. Can you actually subtract 1
from 2 to the power of 18 without a calculator?
Yes, without a calculator.
So the first thing we can do is to simplify this further.
Remember that 18 is the same thing as 9 multiplied by 2.
18 is 9 multiplied by 2.
Therefore,
we can rewrite this as 2 to the power of 9 multiplied by 2.
minus 1 okay
but recall that a to the power of m
multiplied by n is the same thing as a to the power of m
raised to the power of n therefore we can write this as
2 to the power of 9 raised to the power of 2
minus 1 please subscribe to my channel if this is the first time
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accordingly when necessary now note that one
is the same thing as one squared right
therefore i can express these two terms as squares
so we have two to the power of nine
raised to the power of 2 minus 1 squared okay
so now we have difference of two
squares where it said that x squared minus
y squared is equal to x plus y
multiplied by x minus y therefore we can write
this as 2 to the power of 9 plus 1
multiplied by two to the power of nine minus one okay
so it's time to break two to the power of
nine down um two to the power of nine
is the same thing as two times two times two times two
times two times two times two times two times
two one two three four five six seven eight nine
right now 2 times 2 is 4 4 times 2 is 8 8 times 2
is 16 16 times 2 is 32 32 times 2 is 64
64 times 2 should be 120 plus 8 that should be
128 so 128 times 4 let's use 4 2 times 2 let's see
we have to carry one carry three rather four times two
is eight plus three is eleven carry one
four times one is four plus one five
so we have 512 so we have 512
plus one just see put and see
how we're going to simplify
this very well okay so we have 512 plus one
and 512 minus one so
this will be equal to let's write this as 513 right
and this one has 511 to solve this faster i would
rather write this as 500 plus 13
and this has 500 plus 11 all right
so now this will be 500 times
500 multiplied by 500
then 500 times 11 right plus 500 times
11 plus 13 times 500 500 times 13
plus 13 times 11 13 multiplied
by 11 now let's simplify 5 times 5
is 25 we add four zeros 1 2
3 4 plus 5 plus 5 5 plus 0 is 5
so we have 5 5 0 0 plus 500 times
13 13 times 5 this should be
5 carry 1 so we have 65 right
so we write 65 and add the two zeros
then 13 times 11 1 plus 3 is 4
so 143 now we can add so
we have two 250 000 add
5 500 add 6 500 add 143
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so that you don't miss my videos all right so we have
zero zero zero and three that means
this is three again we have zero zero zero and four
right we have 10 plus 1 11 carry one now we have
6 6 which is 12 carry one this becomes 6 and this
becomes 2 and that's your answer thank you
for your patience thank you for your cooperation and
thank you for your support i wish to see you
in my next video have a lovely day and bye
