Advertisements
Advertisements
Question
If 34x = ( 81 )-1 and `10^(1/y) = 0.0001, "Find the value of " 2^(- x ) xx 16^y `
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
APPEARS IN
RELATED QUESTIONS
Prove that : `( a + b + c )/( a^-1b^-1 + b^-1c^-1 + c^-1a^-1 ) = abc`
Simplify : `2{m-3(n+overline(m-2n))}`
Simplify : `3"x"-[4"x"-overline(3"x"-5"y")-3 {2"x"-(3"x"-overline(2"x"-3"y"))}]`
Write each of the following in the simplest form:
(a3)5 x a4
Write each of the following in the simplest form:
`"a"^(1/3) ÷ "a"^(-2/3)`
Simplify the following:
`(27 xx^9)^(2/3)`
Simplify the following:
`root(3)(x^4y^2) ÷ root(6)(x^5y^-5)`
Simplify the following:
`{("a"^"m")^("m" - 1/"m")}^(1/("m" + 1)`
Simplify the following:
`(5^x xx 7 - 5^x)/(5^(x + 2) - 5^(x + 1)`
Simplify the following:
`(2^"m" xx 3 - 2^"m")/(2^("m" + 4) - 2^("m" + 1)`
