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the square root of 72x^5y^12

When thinking of exponents, you can always write them in the form

x ^ (raise / root)

So, if you are raising x to a power and also taking a root of it, you can write it like a fraction instead!

Lets look at each term!

75 is raised to the first power and we are taking the square (2) root. So, we can write it as 

75^(1/2)

If we think of square factors of 75, we know that 75 = 25*3. Thus, we can write this as

75^(1/2) = (25*3)^(1/2) = 25^(1/2) * 3^(1/2) = 5 * 3^(1/2) =  5 sqrt(3)

x is raised to the fifth power and we are taking the square (2) root. So, we can write it as 

x^(5/2)

This can be simplified. Lets write this as

x^(4/2 + 1/2) = x^(4/2) * x^(1/2) = x^2 * x^(1/2) =  x^2 sqrt (x)

y is raised to the 12th power and we are taking the square (2) root. So, we can write it as 

y^(12/2)

This fraction can be simplified to

y^(6/1) = y^6

Combining this all together, we get :

5x^2y^6 sqrt (3x)

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