Draw a triangle in the plane with vertices , , and the origin. Then is the angle between the positive x-axis and the ray beginning at the origin and passing through . Therefore, is .

Multiply the numerator by the reciprocal of the denominator.

One to any power is one.

Use the power rule to distribute the exponent.

Apply the product rule to .

Apply the product rule to .

Multiply by by adding the exponents.

Move .

Multiply by .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Raise to the power of .

Raise to the power of .

Raise to the power of .

To write as a fraction with a common denominator, multiply by .

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Multiply by .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Subtract from .

Rewrite as .

Simplify the numerator.

Rewrite as .

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

Simplify the denominator.

Rewrite as .

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

Multiply the numerator by the reciprocal of the denominator.

Multiply by .

Move the leading negative in into the numerator.

Cancel the common factor.

Rewrite the expression.

Combine and .

Move the negative in front of the fraction.

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Find the Exact Value tan(arcsin(-5/13))