# Evaluate square root of -27* square root of -27 -27⋅-27
Rewrite -27 as -1(27).
-1(27)⋅-27
Rewrite -1(27) as -1⋅27.
-1⋅27⋅-27
Rewrite -1 as i.
i⋅27⋅-27
Rewrite -27 as -1(27).
i⋅27⋅-1(27)
Rewrite -1(27) as -1⋅27.
i⋅27⋅(-1⋅27)
Rewrite -1 as i.
i⋅27⋅(i⋅27)
Rewrite 27 as 32⋅3.
Factor 9 out of 27.
i⋅9(3)⋅(i⋅27)
Rewrite 9 as 32.
i⋅32⋅3⋅(i⋅27)
i⋅32⋅3⋅(i⋅27)
Pull terms out from under the radical.
i⋅(33)⋅(i⋅27)
Move 3 to the left of i.
3⋅i3⋅(i⋅27)
Rewrite 27 as 32⋅3.
Factor 9 out of 27.
3i3⋅(i⋅9(3))
Rewrite 9 as 32.
3i3⋅(i⋅32⋅3)
3i3⋅(i⋅32⋅3)
Pull terms out from under the radical.
3i3⋅(i⋅(33))
Move 3 to the left of i.
3i3⋅(3⋅i3)
Multiply 3i3(3i3).
Multiply 3 by 3.
9i3(i3)
Raise i to the power of 1.
9(i1i)33
Raise i to the power of 1.
9(i1i1)33
Use the power rule aman=am+n to combine exponents.
9i1+133
Add 1 and 1.
9i233
Raise 3 to the power of 1.
9i2(313)
Raise 3 to the power of 1.
9i2(3131)
Use the power rule aman=am+n to combine exponents.
9i231+1
Add 1 and 1.
9i232
9i232
Rewrite i2 as -1.
9⋅-132
Multiply 9 by -1.
-932
Rewrite 32 as 3.
Use axn=axn to rewrite 3 as 312.
-9(312)2
Apply the power rule and multiply exponents, (am)n=amn.
-9⋅312⋅2
Combine 12 and 2.
-9⋅322
Cancel the common factor of 2.
Cancel the common factor.
-9⋅322
Divide 1 by 1.
-9⋅31
-9⋅31
Evaluate the exponent.
-9⋅3
-9⋅3
Multiply -9 by 3.
-27
Evaluate square root of -27* square root of -27

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