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When Simplified ( 256 ) − ( 4 − 3 / 2 ) is - Mathematics

MCQ

When simplified \[(256) {}^{- ( 4^{- 3/2} )}\] is

Options

  • 8

  • \[\frac{1}{8}\]

  • 2

  • \[\frac{1}{2}\]

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Solution

Simplify  `(256)^((-4 3/2)`

 `(256)^((-4 3/2))` =  `(256)^-(2^2)^(3/2)`

                        = `(256)^((-2^(2xx - 3/2))`

                       = `(256)^-(2^(2xx - 3/2))`

`(256)^((-4-^(3/2))` = `(256)^(-(2) ^((-3))`

`(256)^((-4-^(3/2))` = `(256) ^(1/((-2))`

= `(256) ^(1/(-8)`

= `(2^8) ^(1/(-8)`

= `2^(8  xx 1/(-8)`

`(256)^((-4 -3/2)) = 2^(8xx 1/-8) = 1/2`

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 2 Exponents of Real Numbers
Q 29 | Page 32
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