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Miscellaneous Examples Using the Laws of Exponents

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Example

Write exponential form for 8 × 8 × 8 × 8 taking base as 2.

8 × 8 × 8 × 8 = 84
8 = 2 × 2 × 2 = 23
Therefore, 84

= (23)4

= 23 × 23 × 23 × 23

= 23 × 4.........[ (am)n = amn]

= 212

Example

Simplify and write the answer in the exponential form.

[(22)3 x 36] x 56

[(22)3 x 36] x 56

= [26 x 36] x 56

= (2 x 3)6 x 56

= (2 x 3 x 5)6

= 306.

Example

Simplify: `(12^4 xx 9^3 xx 4)/(6^3 xx 8^2 xx 27)`

= `((2^2 xx 3)^4 xx (3^2)^3 xx 2^2)/((2 xx 3)^3 xx (2^3)^2 xx 3^3)`

= `((2^2)^4 xx (3)^4 xx 3^(2 xx 3) xx 2^2)/(2^3 xx 3^3 xx 2^(2 xx 3) xx 3^3)`

= `(2^8 xx 2^2 xx 3^4 xx 3^6)/(2^3 xx 2^6 xx 3^3 xx 3^3)`

= `(2^(8 + 2) xx 3^(4 + 6))/(2^(3 + 6) xx 3^(3 + 3))`

= `(2^10 xx 3^10)/(2^9 xx 3^6)`

= 210 - 9 x 310 - 6

= 21 x 34

= 2 x 81 

= 162.

Example

Simplify: `(2 xx 3^4 xx 2^5)/(9 xx 4^2)`

= `(2 xx 3^4 xx 2^5)/(3^2 xx (2^2)^2)`

= `(2 xx 2^5 xx 3^4)/(3^2 xx 2^(2 xx 2))`

= `(2^(1 + 5) xx 3^4)/(2^4 xx 3^2)`

= `(2^6 xx 3^4)/(2^4 xx 3^2)`

= 26 - 4 x 34 - 2

= 22 x 32

= 4 x 9

= 36.

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Shaalaa.com | Solving Problems Using Laws of Exponents - Part 1

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