Question

The expression \[\sqrt[4]{16x^2y^7}\] is equivalent to

Answer 1

The solution to the problem is as follows:

4 sqrt(16x^2 y^7) 

Protip: sqrt(abc) = sqrt(a)sqrt(b)sqrt(c). Therefore, 

4sqrt(16x^2y^7) = 4sqrt(16)sqrt(x^2)sqrt(y^7) 

We can deal with sqrt(16); it is equal to 4. 

4(4) sqrt(x^2)sqrt(y^7) 
16sqrt(x^2)sqrt(y^7) 

Next, it is a known fact that sqrt(z^2) is the same as |z|, or the absolute value of z. That means 
sqrt(x^2) = |x| 

16|x| sqrt(y^7) 

Split y^7 as y^6 * y 

16|x| sqrt(y^6 * y) 
16|x| sqrt(y^6) sqrt(y) 
16|x| sqrt([y^3]^2) sqrt(y) 
16|x| |y^3| sqrt(y)

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