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Basic Math Examples
√-27⋅√3√−27⋅√3
Step 1
Rewrite -27 as -1(27).
√-1(27)⋅√3
Step 2
Rewrite √-1(27) as √-1⋅√27.
√-1⋅√27⋅√3
Step 3
Rewrite √-1 as i.
i⋅√27⋅√3
Step 4
Step 4.1
Factor 9 out of 27.
i⋅√9(3)⋅√3
Step 4.2
Rewrite 9 as 32.
i⋅√32⋅3⋅√3
i⋅√32⋅3⋅√3
Step 5
Pull terms out from under the radical.
i⋅(3√3)⋅√3
Step 6
Move 3 to the left of i.
3⋅i√3⋅√3
Step 7
Step 7.1
Raise √3 to the power of 1.
3i(√31√3)
Step 7.2
Raise √3 to the power of 1.
3i(√31√31)
Step 7.3
Use the power rule aman=am+n to combine exponents.
3i√31+1
Step 7.4
Add 1 and 1.
3i√32
3i√32
Step 8
Step 8.1
Use n√ax=axn to rewrite √3 as 312.
3i(312)2
Step 8.2
Apply the power rule and multiply exponents, (am)n=amn.
3i⋅312⋅2
Step 8.3
Combine 12 and 2.
3i⋅322
Step 8.4
Cancel the common factor of 2.
Step 8.4.1
Cancel the common factor.
3i⋅322
Step 8.4.2
Rewrite the expression.
3i⋅31
3i⋅31
Step 8.5
Evaluate the exponent.
3i⋅3
3i⋅3
Step 9
Multiply 3 by 3.
9i