Wrong result with exponentiation/inverse?

[Isolus]

I have written some tests to better understand the library. I came across a problem. In my opinion according to the laws of exponentiation ( (a^b)^c = a^(b*c) ), all tests should return true since a^(b * inv(b)) = a. But the second and fourth don't.

Is there a fault in my reasoning or is this a bug?

	key, err := bls.RandFQ12(rand.Reader)
	if err != nil {
		fmt.Println(err)
		return
	}
	k, err := bls.RandFQ(rand.Reader)
	if err != nil {
		fmt.Println(err)
		return
	}
	kInv, b := k.Inverse()
	if !b {
		fmt.Println("no inverse")
		return
	}
	r := k.Copy()
	r.MulAssign(kInv)

	tmp := key.Exp(k.ToRepr()).Exp(kInv.ToRepr())

	fmt.Println("Test 1: ", r.Equals(bls.FQOne))
	fmt.Println("Test 2: ", key.Equals(tmp))

	g := bls.G1AffineOne.Mul(k.ToRepr())
	h := bls.G2AffineOne.Mul(kInv.ToRepr())
	p := bls.Pairing(g, h)
	palt := bls.Pairing(bls.G1AffineOne.ToProjective(), bls.G2AffineOne.ToProjective())

	fmt.Println("Test 3: ", r.Equals(bls.FQOne))
	fmt.Println("Test 4: ", p.Equals(palt))
	fmt.Println("Test 5: ", p.Equals(palt.Exp(k.ToRepr()).Exp(kInv.ToRepr())))