Advertisements
Advertisements
प्रश्न
Simplify the following:
`("a"^(1/3) + "a"^(-1/3))("a"^(2/3) - 1 + "a"^(-2/3))`
Advertisements
उत्तर
`("a"^(1/3) + "a"^(-1/3))("a"^(2/3) - 1 + "a"^(-2/3))`
= `"a"^(1/3)("a"^(2/3) -1 + "a"^(-2/3)) + "a"^(-1/3)("a"^(2/3) - 1 + "a"^(-2/3))`
= `("a"^(1/3) xx "a"^(2/3) - "a"^(1/3) xx 1 + "a"^(1/3) xx "a"^(-2/3)) + ("a"^(-1/3) xx "a"^(2/3) - "a"^(-1/3) xx 1 + "a"^(-1/3) xx "a"^(-2/3))`
= `("a"^(1/3 + 2/3) - "a"^(1/3) xx 1 + "a"^(1/3 + 2/3)) + ("a"^(-1/3 + 2/3) - "a"^(-1/3) + "a"^(-1/3 - 2/3))` .....(Using am x an = am+n)
= `("a"^1 - "a"^(1/3) + "a"^(-1/3)) + ("a"^(1/3) - "a"^(-1/3) + "a"^-1)`
= `"a" - "a"^(1/3) + "a"^(-1/3) + "a"^(1/3) - "a"^(-1/3) + (1)/"a"`
= `"a" + (1)/"a"`.
APPEARS IN
संबंधित प्रश्न
If (am)n = am .an, find the value of : m(n - 1) - (n - 1)
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 : `2{m-3(n+overline(m-2n))}`
Simplify : `3"x"-[3"x"-{3"x"-(3"x"-overline(3"x"-"y"))}]`
Simplify : `2[6 + 4 {"m"-6(7 - overline("n"+"p")) + "q"}]`
Write each of the following in the simplest form:
(a3)5 x a4
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:
`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`
