Advertisements
Advertisements
Question
Simplify the following:
`("a"^(1/3) + "a"^(-1/3))("a"^(2/3) - 1 + "a"^(-2/3))`
Solution
`("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
RELATED QUESTIONS
Evaluate : `(64)^(2/3) - root(3)(125) - 1/2^(-5) + (27)^(-2/3) xx (25/9)^(-1/2)`
If (am)n = am .an, find the value of : m(n - 1) - (n - 1)
Simplify : −3 (1 − x2) − 2{x2 − (3 − 2x2)}
Simplify : `"p"^2"x"-2{"px"-3"x"("x"^2-overline(3"a"-"x"^2))}`
Simplify : `2[6 + 4 {"m"-6(7 - overline("n"+"p")) + "q"}]`
Simplify: `3"a"xx[8"b" ÷ 4-6{"a"-(5"a"-overline(3"b"-2"a"))} ]`
Write the following in the simplest form:
(b-2 - a-2) ÷ (b-1 - a-1)
Simplify the following:
`((36"m"^-4)/(49"n"^-2))^(-3/2)`
Simplify the following:
`(27/343)^(2/3) ÷ (1)/(625/1296)^(1/4) xx (536)/root(3)(27)`
Simplify the following:
`(5^("n" + 2) - 6.5^("n" + 1))/(13.5^"n" - 2.5^("n" + 1)`
