Properties of rational exponents

1. Product of rational exponents

Rewrite the expression in the form .

(defn prod-rat-exp [[[b1 [n1 d1]] [b2 [n2 d2]]]]
    (str b1 "^{" (+ (* n2 d1) (* n1 d2)) "/" (* d1 d2) "}"))

(prod-rat-exp [['b [4 1]] ['b [-1 4]]])

0.0s

Clojure

"b^{15/4}"

(prod-rat-exp [['a [2 5]] ['a [-3 1]]])

0.0s

Clojure

"a^{-13/5}"

(prod-rat-exp [['y [3 4]] ['y [1 3]]])

0.0s

Clojure

"x^{-7/9}"

Rewrite the expression in the form .

Here we have to get it into the right form by converting into .

Rewrite the expression as a sum of terms, where each term is in the form .

2. Quotient of rational exponents

Rewrite the expression in the form .

(defn quot-rat-exp
  [[[b1 [n1 d1] :as n] [b2 [n2 d2] :as d]]]
  (if (= n [1 [1 1]])
    (str b2 "^{" (- n2) "/" d2 "}")
    (str b2 "^{" (str (- (/ n1 d1) (/ n2 d2))) "}")))

(quot-rat-exp [[1 [1 1]] ['x [2 3]]])

0.1s

Clojure

"x^{-2/3}"

Here, we need to first turn into .

Rewrite the expression as a sum of terms, where each term is in the form .

3. Powers of rational exponents

(defn pow-rat-exp
  [[[b [bn bd]] [pn pd]]]
  (if (int? (/ (* bn pn) (* bd pd)))
    (str b "^{" (/ (* pn bn) bd) "}")
    (str b "^{" (* pn bn) "/" (* bd pd) "}")))

(pow-rat-exp [['y [-1 2]] [4 1]])

0.2s

Clojure

"y^{-2}"

(pow-rat-exp [['a [2 3]] [-1 1]])

0.1s

Clojure

"a^{-2/3}"