a³ x a² = a^{3 + 2} = a⁵

4³ x 2³ = (4 x 2)³ = 8³      a^m x b^m = (ab)^m

 l⁴ \(\div\) q⁴ = \(\frac { { l }^{ 4 } }{ { q }^{ 4 } } ={ \left( \frac { l }{ q } \right) }^{ 4 }\)

825

2²x5²

We have, 3 x 4⁴ = 3 x 4 x 4 x 4 x 4 = 3 x 256 = 768
Hence, the value of 3 x 4⁴ is 768

We have, 5³ or 3⁵
\(\therefore\) 5³ = 5 x 5 x 5 = 125 [multiply 5 three times]
and 3⁵ =3 x3 x3 x3 x3= 243 [multiply 3 five times]
\(\because\)243>125 \(\Rightarrow\) 3⁵ > 5³
Hence, 3⁵ is greater than 5³

b x b x b x b = b⁴ [since, b is multiplied 4 times]

6234269

Given, \(\frac { p }{ q } =\left( \frac { 3 }{ 2 } \right) ^{ 2 }\div \left( \frac { 9 }{ 4 } \right) ^{ 0 }\)
∵ \(\left( \frac { 9 }{ 4 } \right) ^{ 0 }=\{ \left( \frac { 3 }{ 2 } \right) ^{ 2 }\} ^{ 0 }=\left( \frac { 3 }{ 2 } \right) ^{ 2\times 0 }=\left( \frac { 3 }{ 2 } \right) ^{ 0 }\)
Now, \(\left( \frac { 3 }{ 2 } \right) ^{ 3 }\div \left( \frac { 3 }{ 2 } \right) ^{ 0 }\)
Let a= \(\frac { 3 }{ 2 } \)
So, \(\frac { p }{ q } =\left( \frac { 3 }{ 2 } \right) ^{ 2-0 }=\left( \frac { 3 }{ 2 } \right) ^{ 2\times 3 }\)    [∵ a^m ÷ aⁿ =a^m-n]
Now, \(\left( \frac { p }{ q } \right) ^{ 3 }=\{ \left( \frac { 3 }{ 2 } \right) ^{ 2 }\} ^{ 3 }=\left( \frac { 3 }{ 2 } \right) ^{ 2x3 }=\left( \frac { 3 }{ 2 } \right) ^{ 6 }\)
= \(\frac { 3\times 3\times 3\times 3\times 3\times 3 }{ 2\times 2\times 2\times 2\times 2\times 2 } =\frac { 729 }{ 64 } \).

Given, \(\frac { 144 }{ 875 } \)
∵ 144 = 2 x 2 x 2 x 2 x 3 x 3 = 2⁴ x 3²
and 875 = 5 x 5 x 5 x 7 = 5³ x 7


The exponent form of \(\frac { 144 }{ 875 } \) is = \(\frac { { 2 }^{ 4 }{ \times { 3 }^{ 2 } } }{ { 5 }^{ 3 }\times 7 } \)

\(-\frac { 4 }{ 5 } \)

Radius of Sun = 700000000 = 7 x 10⁸
and radius of Earth =6400000 =64x10⁵ m =2⁶ x10⁵ m
Then, \(\frac { Radius\ of\ Earth }{ Radius\ of\ Sun } =\frac { { 2 }^{ 6 }\times { 10 }^{ 5 } }{ 7\times { 10 }^{ 8 } } \)
\(=\left( \frac { 64 }{ 7 } \right) \times { 10 }^{ -3 }\) (approx.)

Given, 1.75 x1 0^-3
1.75 = 175 x 10^-2
So, 1.75 x 10^-3 =175 x 10^-3 x 10^-2
=175 x 10^-5          \(\left[ \because \frac { 1 }{ { 10 }^{ 5 } } ={ 10 }^{ -5 } \right] \)
= 0.00175

Area covered by water = 361419000 km²
Area covered by land = 148647000 km²
Convertion of area into scientific notation,
361419000 = 361419 x10³
\(\because\)  361419 = 3,61419 x10⁵
So, 3,61419 x10⁵ x10³ =3,61419 X10⁸
and 148647000 = 148647 x 10³
\(\Rightarrow\)  148647 = 1,48647 x 10⁵
So, 1.48647x10⁵ x10³ =1.48647 X10⁸
Let 3.61419 x 10⁸ \(\approx\)3.6 x10⁸
and 1.48647 X108 \(\approx\) 1.5 x10⁸
\(\therefore\) Ratio of water to land = 3.6/1.5 = 12:5
The value depicted here is that we should use scientific method for easy calculation.