0:00
in this video we're going to compare two
0:02
large numbers 55 raised to the^ of 44
0:07
and 44 raised to the power of
0:10
55 as always before watching further try
0:14
to solve this problem on your own we
0:16
need to compare 55 to the^ of 44 write
0:20
down the comparison sign which will be
0:21
the sign of our future inequality or
0:24
possibly equality and 44 to the power of
0:26
55 notice that both numbers 55 and 44
0:31
are divisible by 11 so it would be
0:33
convenient to take the 11th root of both
0:35
sides of our inequality in this case the
0:38
comparison sign won't change since we
0:40
are dealing with positive numbers
0:43
extracting the 11th root is equivalent
0:45
to raising each side to the power of 1
0:47
11th let's raise both sides to the power
0:49
of 1 11th when raising a power to a
0:52
power you multiply the exponents so in
0:54
the left side after multiplying 44 by 1
0:57
11th we get four on on the right side we
1:01
get five now we can work with the bases
1:05
exponents 55 is equal to 5 * 11 and this
1:09
whole quantity is raised to the 4th
1:11
power 44 is equal to 4 * 11 and this
1:15
whole quantity is raised to the fifth
1:18
power expand the parentheses to get the
1:20
Expressions on the left side we have 5
1:23
to the 4th power * 11 4th power on the
1:27
right side we have 4 5th power * 11 5th
1:30
power we can now divide both sides of
1:33
our inequality by 11 to 4th power on the
1:36
left side we're left with 5 4th power
1:40
while on the right side we have 4 5th
1:42
power * 11 5 4th power is the same as 2^
1:49
625 on the right side 4 5th power is the
1:53
same as 2 the 10th power which equals
1:58
1,24 multiply that by 11 as a result the
2:01
left side is less than the right side
2:04
this means that for the original numbers
2:06
55 raised to the 44th power is less than
2:09
44 ra to the 55th power write the answer
2:14
44 ra to the 55th power is greater than
2:16
55 ra to the 44th power the problem is
2:20
solved if you understood the solution
2:23
give a thumbs up leave a comment and
2:25
don't forget to subscribe to the channel
