Question

2^n+4 - 2.2^n / 2.2^n+3 +2^-3 simplify ​

Answer 1

Answer:

1

Step-by-Step Explanation:

(2ⁿ⁺⁴   - 2.2ⁿ ) /( 2.2ⁿ⁺³) + 1/8

= (2ⁿ.2⁴ - 2.2ⁿ) / (2ⁿ 2⁴)  +  1/8

Taking 2ⁿ common,

= [ 2ⁿ ( 16 - 2 ) / 2ⁿ 2⁴ ] + 1/8

Eliminating in the equation 2ⁿ,

We have,

=  14/16 + 1/8  = 7/8 + 1/8 = 1

Answer 2

Concept

Given a number a that is raised to a negative power say -x, it can be written as

a^-x = 1/(a^x)

Given

(2ⁿ⁺⁴ - 2.2ⁿ ) /( 2.2ⁿ⁺³) + $2^{3}$

Find

we need to simplify the given equation

Solution

We have

(2ⁿ⁺⁴ - 2.2ⁿ ) /( 2.2ⁿ⁺³) + $2^{-3}$

this can be written as

= (2ⁿ.2⁴ - 2.2ⁿ) / (2ⁿ 2⁴)  +  1/8

Taking 2ⁿ common from the numerator we get,

[ 2ⁿ ( 2⁴ - 2 ) / 2ⁿ 2⁴ ] + 1/8

= [ 2ⁿ ( 16 - 2 ) / 2ⁿ 2⁴ ] + 1/8

= [ 2ⁿ ( 14 ) / 2ⁿ 2⁴ ] + 1/8

Eliminating 2ⁿ from numerator and denominator,

[( 14 ) / 2⁴ ]+ 1/8

= 14/16 + 1/8  

= 7/8 + 1/8

= 1

Thus, on simplifying (2ⁿ⁺⁴ - 2.2ⁿ ) /( 2.2ⁿ⁺³) + $2^{3}$ becomes equal to 1.

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