How can I simplify e^(2n ln sin(pi/3))?

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In summary, to simplify a fraction, divide the numerator and denominator by their greatest common factor (GCF). To simplify an algebraic expression, combine like terms by adding or subtracting coefficients with the same variables, use the distributive property to factor out any common factors, and simplify any remaining terms. For simplifying a radical expression, find the factors of the number inside the radical and simplify the perfect square factor while leaving the other factor inside. To simplify an equation with exponents, use the exponent properties to combine like terms and remember the rules for simplifying specific exponents. For simplifying large numbers, use the divisibility rules as a shortcut to break down the number into smaller factors.
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Homework Statement



Simplify e^(2n ln sin(pi/3))

Homework Equations




The Attempt at a Solution



I know that I can simplify to the form e^ln sin(π/3)^2n but I'm stuck there.
I can't see how I could end up with the answer (3/4)^n, which is supposed to be the right answer.
 
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Nevermind I'm a dumbass. Sin(pi/3) = sqrt(3)/2
 

FAQ: How can I simplify e^(2n ln sin(pi/3))?

How do you simplify this fraction?

To simplify a fraction, divide the numerator and denominator by their greatest common factor (GCF). This will result in an equivalent fraction with smaller numbers.

What is the process for simplifying an algebraic expression?

To simplify an algebraic expression, combine like terms by adding or subtracting coefficients with the same variables. Then, use the distributive property to factor out any common factors. Finally, simplify any remaining terms if possible.

Can you give an example of simplifying a radical expression?

For example, to simplify √24, first find the factors of 24. √24 = √(4 x 6). Then, take the square root of the perfect square factor (4) and leave the other factor (6) inside the radical. Therefore, √24 = 2√6.

How do you simplify an equation with exponents?

To simplify an equation with exponents, use the exponent properties to combine like terms. For example, x^2 * x^3 = x^(2+3) = x^5. Also, remember that x^0 = 1 and x^1 = x.

Is there a shortcut for simplifying large numbers?

Yes, there is a shortcut known as the divisibility rules. For example, a number is divisible by 2 if the last digit is even, and a number is divisible by 3 if the sum of its digits is divisible by 3. These rules can help simplify large numbers by breaking them down into smaller factors.

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