Question

Simplify and write in exponential forms .( 2 power 5 - 2 power 8 ) × 2 power -5​

Answer 1

$\Large \fbox \red {Question \: :}$

Simplify and write in exponential forms :

$( {2}^{5} - {2}^{8} ) \times {2}^{ - 5}$

$\Large \fbox \red {Answer \: :}$

$( {2}^{5} - {2}^{8} ) \times {2}^{ - 5}$

• First we have to factorize

$( {2}^{5} - {2}^{8} )$

$= {2}^{5} (1 - {2}^{3} )$

$= 32(1 - 8)$

$= 32 \times - 7$

$= - 224$

• Then, we have to multiply the equation.

$= - 224 \times {2}^{ - 5}$

$= - 224 \times( \frac{1}{2} ) {}^{5}$

$= - 224 \times \frac{1}{32}$

$= - 7$

$\implies$ So, our answer is - 7.

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