Rewrite as .

Factor the perfect power out of .

Factor the perfect power out of .

Rearrange the fraction .

Pull terms out from under the radical.

Rewrite as .

Multiply by .

Combine and simplify the denominator.

Multiply and .

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Rewrite as .

Use to rewrite as .

Apply the power rule and multiply exponents, .

Combine and .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Evaluate the exponent.

Combine using the product rule for radicals.

Multiply .

Multiply and .

Multiply by .

Cancel the common factor of .

Factor out of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Combine and .

Move to the left of .

To rewrite as a function of , write the equation so that is by itself on one side of the equal sign and an expression involving only is on the other side.

Write as a Function of L t=2pi square root of L/32