16²⁵ = (24)²⁵ = 2¹⁰⁰
8¹⁰⁰ = (2³)¹⁰⁰ = 2³⁰⁰ = (2³)¹⁰⁰ = 8¹⁰⁰
3⁵⁰⁰ = (35)¹⁰⁰ = (243)¹⁰⁰
4⁴⁰⁰ = (22)⁴⁰⁰ = 2⁸⁰⁰ = (2⁸)¹⁰⁰ = (256)¹⁰⁰
2¹⁰⁰ = (2⁶)¹⁰⁰ = (64)¹⁰⁰
2¹⁰⁰ < 8¹⁰⁰ < 64¹⁰⁰ < 243¹⁰⁰ < 256¹⁰⁰
Order from the least to the greatet
16²⁵, 8¹⁰⁰, 2⁶⁰⁰,3⁵⁰⁰,4⁴⁰⁰

\(\sqrt { 286225 } \) 

\(\sqrt { 286225 } =535\) 
\(\sqrt { 2862.5 } =53.5\) 
\(\sqrt { 28.6225 } =5.35\) 
\(\sqrt { 2862.5 } +\sqrt { 28.6225 } =53.5+5.35\) 
= 58.85

Total number of cadets = 1536

If we take 39 x 39 cadets
15 cadets would be remained,
So square design should be 40 x 40
40 x 40 = 1600
. Number of cadets would be
required = 1600 - 1536 = 64

Area of the greeting card = 90cm²
= 9 x 10cm²
The length of its side are 9cm and 10 cm.

Thr radius of a hydrogen atom is,
2.5 x 10^-11m
Standard notation,
0.000000000025 m.

\(\left( { 2 }^{ -1 }\times { 3 }^{ -1 } \right) \div { 6 }^{ -1 }\) 
\(\left( \cfrac { 1 }{ 2 } \times \cfrac { 1 }{ 3 } \right) \div \cfrac { 1 }{ 6 } \) 

(2 x 3)^-1 + 6^-2
\(\cfrac { { 6 }^{ -1 } }{ { 6 }^{ -2 } } ={ 6 }^{ -1+2 }={ 6 }^{ 1 }=6\)

-3

   \(\left( \cfrac { 1 }{ 2 } \right) ^{ -5 }=\cfrac { 1 }{ { 2 }^{ 3 } } ={ 2 }^{ 5 }=2\times 2\times 2\times 2\times 2=32\)

200 = 2 x 2 x 2 x 5 x 5
We have one triplets. We need one more 5 to get another triplet.
5 should be multiplied to make 200 a perfect cube.