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