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Q.

The value of ( 2 5 ÷ 2 8 )× 2 −7   is[[1]].


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Detailed Solution

The value of ( 2 5 ÷ 2 8 )× 2 −7   is 1 1024  .
We have ( 2 5 ÷ 2 8 )× 2 −7  
Using law of exponent x −m = 1 x m   in the above expression.
⇒( 2 5 ÷ 2 8 )× 2 −7 =( 2 5 ÷ 2 8 )× 1 2 7  
⇒ 2 5 2 8 × 1 2 7  
⇒ 2 5 2 8 × 2 7  
 Using law of exponent x m × x n = x m+n   in above expression
⇒( 2 5 ÷ 2 8 )× 2 −7 = 2 5 2 8+7  
⇒ 2 5 2 15  
 Using law of exponent x m x n = x m−n   in above expression
⇒ 2 5−15  
⇒ 2 −10   Using law of exponent  x −m = 1 x m   in above expression
⇒( 2 5 ÷ 2 8 )× 2 −7 = 1 2 10  
⇒ 1 2×2×2×2×2×2×2×2×2×2  
⇒ 1 1024  
Thus, the correct value is 1 1024  .  
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The value of ( 2 5 ÷ 2 8 )× 2 −7   is[[1]].