Advertisements
Advertisements
प्रश्न
Simplify the following:
`root(3)(x^4y^2) ÷ root(6)(x^5y^-5)`
Advertisements
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
Solve : 3(2x + 1) - 2x+2 + 5 = 0.
Evaluate :
`[ 2^n xx 6^(m + 1 ) xx 10^( m - n ) xx 15^(m + n - 2)]/[4^m xx 3^(2m + n) xx 25^(m - 1)]`
Simplify : a2 − 2a + {5a2 − (3a - 4a2)}
Simplify : `2[6 + 4 {"m"-6(7 - overline("n"+"p")) + "q"}]`
Write each of the following in the simplest form:
a-3 x a2 x a0
Simplify the following:
`(8 xx^6y^3)^(2/3)`
Simplify the following:
`((64"a"^12)/(27"b"^6))^(-2/3)`
Simplify the following:
`((36"m"^-4)/(49"n"^-2))^(-3/2)`
Simplify the following:
`("a"^(1/3) + "a"^(-1/3))("a"^(2/3) - 1 + "a"^(-2/3))`
Simplify the following:
`(27/343)^(2/3) ÷ (1)/(625/1296)^(1/4) xx (536)/root(3)(27)`
