# Simplify ( square root of fourteen(cos(one hundred twenty) plus i times sin(one hundred twenty))) to the power of four

Use the reference angle by calculating the angle with equivalent triginometric values in the Initially quadrant. Should be rewritten the expression as a negative one since cosine is negative in the 2nd quadrant.

The exact value of is .

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

The exact value of is .

Use the distributive law.

Add and .

Combine and .

Add using the product rule for radicals.

Multiply by .

Apply the binomial theorem.

Simplify each term.

Apply the power rule for exponent distribution.

Apply the product rule to .

Apply the product rule to .

Raise to the power of .

Multiply by .

Clarify the numerator.

Rewrite as .

Rewrite as .

Use the power rule when multiplying the exponents, .

Combine and .

The common factor should be canceled of and .

Factor out of .

The common factors should be canceled.

Factor out of .

Cancel the common factor.

Reformulate the expression.

First, divide by .

Raise to the power of .

Raise to the power of .

The common factor should be canceled and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

The common factor should be canceled.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Use the power rule to distribute the exponent.

Apply the product rule to .

Apply the product rule to .

Raise to the power of .

Simplify the numerator.

Rewrite as .

Raise to the power of .

Rewrite as .

Factor out of .

Rewrite as .

Withdraw terms from under the radical.

Raise to the power of .

Cancel the common factor of .

Move the leading negative in into the numerator.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Put the negative in front of the fraction.

Multiply .

Combine and .

Combine using the product rule for radicals.

Multiply by .

Combine and .

Simplify the numerator.

Rewrite as .

Factor out of .

Rewrite as .

Pull terms out from under the radical.

First, multiply by .

The common factor should be canceled and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Divide by .

Move to the left of .

Multiply by .

Use the power rule to distribute the exponent.

Apply the product rule to .

Apply the product rule to .

Raise to the power of .

Multiply by .

Rewrite as .

Rewrite as .

Apply the power rule and multiply exponents, .

Combine and .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Solve the exponent.

Raise to the power of .

Cancel the common factor of .

Factor out of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Combine and .

Multiply by .

Divide by .

Use the power rule to distribute the exponent.

Apply the product rule to .

Apply the product rule to .

Simplify the numerator.

Rewrite as .

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.

Rewrite as .

Raise to the power of .

Multiply by .

The common factor should be canceled and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Move the negative in front of the fraction.

Multiply .

Multiply by .

Combine and .

Multiply by .

Move the negative in front of the fraction.

Cancel the common factor of .

Move the leading negative in into the numerator.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Multiply by .

Use the power rule to distribute the exponent.

Apply the product rule to .

Apply the product rule to .

Simplify the numerator.

Rewrite as .

Raise to the power of .

Rewrite as .

Factor out of .

Rewrite as .

Pull terms out from under the radical.

Factor out .

Rewrite as .

Rewrite as .

Add exponents.

Factor out negative.

Multiply by .

Raise to the power of .

Cancel the common factor of .

Factor out of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Combine and .

Combine using the product rule for radicals.

Multiply by .

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Simplify the numerator.

Rewrite as .

Factor out of .

Rewrite as .

Pull terms out from under the radical.

Multiply by .

The common factor should be canceled and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Divide by .

Multiply by .

Use the power rule to distribute the exponent.

Apply the product rule to .

Apply the product rule to .

Simplify the numerator.

Rewrite as .

Rewrite as .

Apply the power rule and multiply exponents, .

Combine and .

The common factor should be canceled and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Divide by .

Raise to the power of .

Rewrite as .

Rewrite as .

Rewrite as .

Raise to the power of .

Raise to the power of .

Multiply by .

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Simplify terms.

Add fractions with similar denominators.

Add and .

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Move the negative in front of the fraction.

Add fractions with the same denominators.

Clarify the expression.

Subtract from .

Divide by .

Shift the factors of .

Add and .

Reorder and .

Do you need help with solving Simplify ( square root of 14(cos(120)+i*sin(120)))^4? We can help you. You can write to our math experts in our application. The best solution for you is above on this page.