Question

Solve Step-by-step
1) (2^55+2^60) - (2^97+2^18)​

Answer 1

Given:-

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$\bf \implies( {2}^{55} + {2}^{60} ) - ({2}^{97} + {2}^{18} )$

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To Find:-

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$\bf \implies The \: Solution$

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STEP BY STEP EXPLANATION:-

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$\bf \implies((1 + {2}^{5} ) \times {2}^{55} ) - ({2}^{97} + {2}^{18} )$

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$\bf \implies((1 + {2}^{5} ) \times {2}^{55} ) - {2}^{97} - {2}^{18}$

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$\bf \implies((1 + 32 ) \times {2}^{55} ) - {2}^{97} - {2}^{18}$

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$\bf \implies(33 \times {2}^{55} ) - {2}^{97} - {2}^{18}$

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$\bf \implies33 \times {2}^{55} - {2}^{97} - {2}^{18}$

Answer 2

To Solve -

Solve the following exponential -

[ 2⁵⁵ + 2⁶⁰ ] - [ 2⁹⁷ + 2¹⁸ ]

Solution -

Here the following exponential is given -

[ 2⁵⁵ + 2⁶⁰ ] - [ 2⁹⁷ + 2¹⁸ ]

Solving -

[ 2⁵⁵ + 2⁶⁰ ] - [ 2⁹⁷ + 2¹⁸ ]

=> 2⁵⁵ + 2⁶⁰ - 2⁹⁷ - 2¹⁸

Grouping similar terms -

=> [ 2⁵⁵ - 2⁹⁷ ] + [ 2⁶⁰ - 2¹⁸ ]

=> 2⁵⁵ [ 1 - 2⁴² ] + 2¹⁸ [ 2⁴² - 1 ]

=> 2⁵⁵ [ 1 - 2⁴² ] - 2¹⁸ [ 1 - 2⁴² ]

=> [ 1 - 2⁴² ][ 2⁵⁵ - 2¹⁸ ]

=> [ 1 - 2⁴² ] [ 2¹⁸ { 2³⁷ - 1 } ]

=> 2¹⁸ [ 1 - 2⁴² ][ 2³⁷ - 1 ] .

This is the required answer.

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Additional Information -

x^a × x^b = x^( a + b ).

x^a / x^b = x^(a - b ) .

[n]√a^k = a^(k/n) .

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