-9⋅-81

Rewrite -9 as -1(9).

-1(9)⋅-81

Rewrite -1(9) as -1⋅9.

-1⋅9⋅-81

Rewrite -1 as i.

i⋅9⋅-81

Rewrite -81 as -1(81).

i⋅9⋅-1(81)

Rewrite -1(81) as -1⋅81.

i⋅9⋅(-1⋅81)

Rewrite -1 as i.

i⋅9⋅(i⋅81)

Rewrite 9 as 32.

i⋅32⋅(i⋅81)

Pull terms out from under the radical, assuming positive real numbers.

i⋅3⋅(i⋅81)

Move 3 to the left of i.

3⋅i⋅(i⋅81)

Rewrite 81 as 92.

3i⋅(i⋅92)

Pull terms out from under the radical, assuming positive real numbers.

3i⋅(i⋅9)

Move 9 to the left of i.

3i⋅(9⋅i)

Multiply 9 by 3.

27ii

Raise i to the power of 1.

27(i1i)

Raise i to the power of 1.

27(i1i1)

Use the power rule aman=am+n to combine exponents.

27i1+1

Add 1 and 1.

27i2

27i2

Rewrite i2 as -1.

27⋅-1

Multiply 27 by -1.

-27

Multiply square root of -9* square root of -81