Answer:
m = 2 and n = 3
Step-by-step explanation:
We want to find the value of the integers m and n that will make the given expression true
(2x^ny^2)^m = 4x^6y^4
We can rewrite the left hand side of the equation as follows;
(2x^3y^2)^2
we can proceed to use inspection to ind the value of m and n
Through inspection since the left hand side of the equation now looks like the right hand side;
Then;
m= 2 and n = 3
Step-by-step explanation:
2:3
It won't allow me to put the answer in the answer part.
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The rows add up to
, respectively. (Notice they're all powers of 2)
The sum of the numbers in row
is
.
The last problem can be solved with the binomial theorem, but I'll assume you don't take that for granted. You can prove this claim by induction. When
,
so the base case holds. Assume the claim holds for
, so that
Use this to show that it holds for
.
Notice that
So you can write the expansion for
as
and since
, you have
and so the claim holds for
, thus proving the claim overall that
Setting
gives
which agrees with the result obtained for part (c).
Least to Greatest:
1/5, 3/10, 6/5, 3/2
Or simplified in decimal form:
0.2, 0.4, 1.2, 1.5