Question

If 3^4x = ( 81 )^-1 and `10^(1/y) = 0.0001, "Find the value of " 2^(- x ) xx 16^y `

Answer 1

3^4x = ( 81 )^-1 and `10^(1/y)` = 0.0001

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

⇒ 3^4x = `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