jaber wrote:
Quantity A |
Quantity B |
(0.822)∗(0.823) |
(0.826) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
I was thinking that the correct answer is B because the exponent of (0.82^6) is 6 which mean is multiplied by itself 6 times which is bigger than (0.82^5) which has the same base and only multiplied by itself 5 times only , that what I thought but I found that the correct answer is A !!!
is it because decimals and fractions power smallest number would be bigger ? unlike the integer number ??
I mean when we compare (2^5) with (2^6) we clearly see that
(2^5) = 32
(2^6) = 64
which means without doubt that (2^6) with the bigger exponents is bigger since the bases are the same in the two values , why the case in the question is totally different ???
Please help
Thank you very much
Remind the following properties.
Case 1:
0<x<1We have
⋯>1/x2>1/x>1>√x>x>x2>x3>⋯.
When a base is between
0 and
1, as exponents grow, they get smaller.
Case 2:
x>1We have
⋯<1/x2<1/x<1<√x<x<x2<x3<⋯.
When a base is greater than
1, as exponents grow, they get bigger.
(ax)y=axy and
ax⋅ay=ax+y.
Since we have
5<6 and
0<0.82<1, we have
(0.82)5>(0.82)6.
Thus, we have
A=(0.82)2⋅(0.82)3=(0.82)5>B=(0.82)6.
Therefore, A is the right answer.