Advertisements
Advertisements
Question
Simplify the following:
`("a"^(1/3) + "a"^(-1/3))("a"^(2/3) - 1 + "a"^(-2/3))`
Advertisements
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
Solve for x : (13)√x = 44 - 34 - 6
If 34x = ( 81 )-1 and `10^(1/y) = 0.0001, "Find the value of " 2^(- x ) xx 16^y `
Prove that : `( a + b + c )/( a^-1b^-1 + b^-1c^-1 + c^-1a^-1 ) = abc`
Evaluate : `((x^q)/(x^r))^(1/(qr)) xx ((x^r)/(x^p))^(1/(rp)) xx ((x^p)/(x^q))^(1/(pq))`
Simplify : −3 (1 − x2) − 2{x2 − (3 − 2x2)}
Simplify: (y3 − 5y2) ÷ y × (y − 1)
Simplify the following:
`((36"m"^-4)/(49"n"^-2))^(-3/2)`
Simplify the following:
`(81)^(3/4) - (1/32)^(-2/5) + 8^(1/3).(1/2)^-1. 2^0`
Simplify the following:
`(3^(x + 1) + 3^x)/(3^(x + 3) - 3^(x + 1)`
Simplify the following:
`(5^("n" + 2) - 6.5^("n" + 1))/(13.5^"n" - 2.5^("n" + 1)`
