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If 34x = ( 81 )-1 and 10^(1/Y) = 0.0001, "Find the Value of " 2^(- X ) Xx 16^Y - Mathematics

Sum

If 34x = ( 81 )-1 and `10^(1/y) = 0.0001, "Find the value of " 2^(- x ) xx 16^y `

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Solution

34x = ( 81 )-1 and `10^(1/y)` = 0.0001

⇒ 34x = `( 3^4 )^-1 and 10^(1/y) = 1/10000`

⇒ 34x = `3^-4 and 10^(1/y) = 1/10^4`

⇒ 4x = - 4 and `10^(1/y) = 10^-4`

⇒ x = - 1 and `1/y` = - 4

⇒ x = - 1 and y = `-1/4`

∴ `2^-x xx 16^y = 2^(-(-1)) x 16^(-1/4)`

= ` 2 xx 2^( 4 xx - 1/4 )`

= ` 2 xx 2^-1`

= `2^(1 - 1)`

= `2^0` 
= 1

Concept: Simplification of Expressions
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APPEARS IN

Selina Concise Mathematics Class 9 ICSE
Chapter 7 Indices (Exponents)
Exercise 7 (C) | Q 9 | Page 101
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