Find five examples, where a number is expressed in exponential form. Also, identify the base and the exponent in each case.

5

(a)

Express the following in usual form.
1.75 x 10^-3

5

(a)

Simplify \(\frac { { 5 }^{ -2 }\times { 3 }^{ -3 }\times (125)^{ 2/3 } }{ (27)^{ -2/3 }\times (32)^{ -1/5 } } \).

5

(a)

Find the value of x, such that \({ \left( \frac { 1 }{ 5 } \right) }^{ 5 }\times { \left( \frac { 1 }{ 5 } \right) }^{ 19 }={ \left( \frac { 1 }{ 5 } \right) }^{ 8x }\) .

5

(a)

Using laws of exponents simplify the following.
\(\frac { \left( -\frac { 3 }{ 4 } \right) ^{ 4 }\times \left( \frac { 125 }{ 27 } \right) }{ \left( \frac { 5 }{ 3 } \right) ^{ 2 }\times \left( \frac { 9 }{ 16 } \right) } \).

5

(a)

If the distance between Earth and Moon is 384000000 m and the distance between the Sun and the Earth is 146900000000 m. Then, which have more distance moon or Sun from Earth. Explain it with the help of standard form of the number.

5

(a)

Simplify:
(i) \({ \left[ { \left\{ { \left( -\frac { 1 }{ 4 } \right) }^{ 2 } \right\} }^{ -2 } \right] }^{ -1 }\)
(ii) \({ \left( -\frac { 3 }{ 2 } \right) }^{ 3 }\div { \left( -\frac { 3 }{ 2 } \right) }^{ 6 }\)

5

(a)

Express the following numbers in standard form.
(i) 31865000000
(ii) 3908.78

5

(a)

A googol is the number 1 followed by 100 zeroes.
(a) How is a googol written as a power?
(b) How is a googol times a googol written as a pawer?

5

(a)

Express the following in exponential form:
[(2³)² x 3⁶]. X 5⁶

5

(a)