This is going to be a piece of
cake for you.
OK, any number (let's call it "n") to any power (let's call
the power "x") is simply the number times itself x times.
An example would be, 3 to the 4th power (written 
would
be 3 times itself four times. That means 3 x 3 x 3 x 3.
Be careful, and don't mistake that for 3 x 4. It is very different. 3 x 4
is 12. But 3 x 3 x 3 x 3 is 81. Big difference! Numbers raised to powers can
grow very large very quickly.
A good rule of thumb, is when you see n to the x power, write
the n down x times, and put multiplication signs between them.
In the above case, we wrote the number 3 down four times, and put multiplication
signs between them.
One more rule is that any number raised to the first power is the original
number itself. For example:
- 3 to the 1st power (written
)
is 3, - 5 to the 1st power (written
)
is 5, - 9 to the 1st power is 9 (written
)
, and so on.
Now to your question:
Using what we have just learned, we can represent your question (which was
2 to the power of x + x = 6) as 
+x
= 6.
Since the numbers in question are
fairly small, a good way to start is by trial and error. Substitute numbers
for x. Let's try x =1.
+
x = 
+ 1
2 to the 1st power is 2, and 2 +1 does not equal 6, so x = 1 won't
work.
Try x = 2. That means +
x = 
+ 2
is
2 times 2.
2 times 2 is 4.
4 + 2 DOES equal 6, which would make your equation true. So x = 2.
You have solved the problem.
I will tell you a secret of a lot
of good mental calculators and other interesting people: It pays to memorize
the powers of 2 up to 2 to the tenth power. It is not hard, and will eventually
help you in a lot of math in your life, if you stick with learning math. Try
it. Write the powers of two out to the tenth power, and look at them for a
few minutes a day.
It will also definitely help you out on some standardized test one day, not
to mention impress your teachers.
I hope the answer can help you.
Hi-ho!
Professor Homunculus