Find the greatest number among (2)
1/3
,(3)
1/2
,1,(5)
1/6
.
- A(2)
1/3 - B(3)
1/2 - C1
- D(5)
1/6
Solution & Step-by-step Explanation
To compare the numbers (2)
1/3
, (3)
1/2
, 1, and (5)
1/6
, we make their fractional exponents have a common denominator.
The denominators of the powers are 3,2,1, and 6.
The LCM of 3,2, and 6 is 6.
Now, raise each number to the power of 6:
((2)
1/3
)
6
=2
2
=4
((3)
1/2
)
6
=3
3
=27
(1)
6
=1
((5)
1/6
)
6
=5
1
=5
Comparing the values: 1<4<5<27.
The greatest value is 27, which corresponds to (3)
1/2
.
1/3
, (3)
1/2
, 1, and (5)
1/6
, we make their fractional exponents have a common denominator.
The denominators of the powers are 3,2,1, and 6.
The LCM of 3,2, and 6 is 6.
Now, raise each number to the power of 6:
((2)
1/3
)
6
=2
2
=4
((3)
1/2
)
6
=3
3
=27
(1)
6
=1
((5)
1/6
)
6
=5
1
=5
Comparing the values: 1<4<5<27.
The greatest value is 27, which corresponds to (3)
1/2
.