81x

Rewrite 81x as 81x.

81x

Rewrite 81 as 92.

92x

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

9x

9x

Multiply 9x by xx.

9x⋅xx

Multiply 9x and xx.

9xxx

Raise x to the power of 1.

9xx1x

Raise x to the power of 1.

9xx1x1

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

9xx1+1

Add 1 and 1.

9xx2

Rewrite x2 as x.

Use axn=axn to rewrite x as x12.

9x(x12)2

Apply the power rule and multiply exponents, (am)n=amn.

9xx12⋅2

Combine 12 and 2.

9xx22

Cancel the common factor of 2.

Cancel the common factor.

9xx22

Divide 1 by 1.

9xx1

9xx1

Simplify.

9xx

9xx

9xx

Divide square root of 81/x