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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)