Aptitude - Surds and Indices - Discussion
Discussion Forum : Surds and Indices - General Questions (Q.No. 6)
6.
(256)0.16 x (256)0.09 = ?
Answer: Option
Explanation:
(256)0.16 x (256)0.09 = (256)(0.16 + 0.09)
= (256)0.25
= (256)(25/100)
= (256)(1/4)
= (44)(1/4)
= 44(1/4)
= 41
= 4
Discussion:
15 comments Page 1 of 2.
Stacy said:
9 months ago
Why do we divide it by 100? Anyone, please explain to me.
Priya said:
1 year ago
(256)0.16 x (256)0.09.
= (256)^(0.16 + 0.09)
= (256)^0.25
= (256)^(0.25/100)
= (256)^25/100
= (256)^(1/4)
= (16²)^(1/4)
16² can be written as (4²)².
= (4⁴)^1/4.
= 4^4×1/4.
Cancellation of powers we get answer as 4.
Another Method :
= (256)^0.25.
= (16²)^0.25 --> ( multiplication of powers 2×0.25),
= (16)^0.50,
= (4²)^0.50 --> ( multiplication of powers 2×0.50)
= 4¹.
= 4.
= (256)^(0.16 + 0.09)
= (256)^0.25
= (256)^(0.25/100)
= (256)^25/100
= (256)^(1/4)
= (16²)^(1/4)
16² can be written as (4²)².
= (4⁴)^1/4.
= 4^4×1/4.
Cancellation of powers we get answer as 4.
Another Method :
= (256)^0.25.
= (16²)^0.25 --> ( multiplication of powers 2×0.25),
= (16)^0.50,
= (4²)^0.50 --> ( multiplication of powers 2×0.50)
= 4¹.
= 4.
Nini said:
3 years ago
Formula used here (a^n x a^m= a^m+n).
Here (^) denotes power*.
~ 256^0.16 x 256^0.09.
~(2^8)^0.16 x (2^8)^0.09.
~(2)^8*0.16 X (2)^8*0.09 multiplying the powers.
~(2)^1.28 X (2)^0.72.
~2^(1.28 +0.75).
>since a^n x a^m =a^m+n.
~2^2=4.
Here (^) denotes power*.
~ 256^0.16 x 256^0.09.
~(2^8)^0.16 x (2^8)^0.09.
~(2)^8*0.16 X (2)^8*0.09 multiplying the powers.
~(2)^1.28 X (2)^0.72.
~2^(1.28 +0.75).
>since a^n x a^m =a^m+n.
~2^2=4.
Srinish said:
5 years ago
Nice explanation @Prasanthi.
Geelani said:
5 years ago
256^(0.16+0.09) = 256^0.25.
256^1/4,
16^2^1/4,
16^1/2 = √16 = 4.
Hence Answer 4.
256^1/4,
16^2^1/4,
16^1/2 = √16 = 4.
Hence Answer 4.
Shree said:
6 years ago
I too agree it is 64.
(1)
Vishnu said:
6 years ago
I think the answer is 64 because 4 th root of 256 is = 64 So answer is 64.
(1)
Afroza said:
6 years ago
Thanks all for your explanation.
Swastika said:
7 years ago
Nice explanation. Thanks.
Gagan Deep kaur said:
8 years ago
Nice explanation. Thank you all.
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