Advertisements
Advertisements
प्रश्न
Simplify the following:
`root(3)(x^4y^2) ÷ root(6)(x^5y^-5)`
उत्तर
`root(3)(x^4y^2) ÷ root(6)(x^5y^-5)`
= `(x^4y^2)^(1/3) ÷ (x^5y^-5)^(1/6)`
= `(x^(4xx1/3)y^(2xx1/3)) ÷ (x^(5xx1/6)y^(-5xx1/6))` .....(Using (am)n = amn)
= `(x^(4/3)y^(2/3)) ÷ (x^(5/6)y^(-5/6))`
= `(x^(4/3)y^(2/3))/(x^(5/6)y^(-5/6))`
= `x^(4/3 - 5/6)y^(2/3 - (-5/6)` .....(Using (am)n = amn)
= `x^(1/2)y^(3/2)`
= `x^(1/2)(y^3)^(1/2)` .....(Using (am)n = amn)
= `sqrt(x) sqrt(y^3)`
= `sqrt(xy^3)`.
APPEARS IN
संबंधित प्रश्न
If 34x = ( 81 )-1 and `10^(1/y) = 0.0001, "Find the value of " 2^(- x ) xx 16^y `
Simplify : `"x" − "y" − {"x" − "y" − ("x" + "y") −overline("x"-"y")}`
Simplify : −3 (1 − x2) − 2{x2 − (3 − 2x2)}
Simplify : `2{m-3(n+overline(m-2n))}`
Simplify : `3"x"-[3"x"-{3"x"-(3"x"-overline(3"x"-"y"))}]`
Simplify : `3"x"-[4"x"-overline(3"x"-5"y")-3 {2"x"-(3"x"-overline(2"x"-3"y"))}]`
Simplify the following and express with positive index:
3p-2q3 ÷ 2p3q-2
Simplify the following:
`x^("m" + 2"n"). x^(3"m" - 8"n") ÷ x^(5"m" - 60)`
Simplify the following:
`(81)^(3/4) - (1/32)^(-2/5) + 8^(1/3).(1/2)^-1. 2^0`
Simplify the following:
`(2^"m" xx 3 - 2^"m")/(2^("m" + 4) - 2^("m" + 1)`
