Question

Help!
Which expression is equivalent?
On edge

Answer 1

Answer: Choice B

`x^(1/8)y^(8)`

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Step-by-step explanation:

The two rules we use are

`(a*b)^c = a^c*b^c`

`(a^b)^c = a^(b*c)`

When applying the first rule to the expression your teacher gave you, we can say that:

`\left(x^(1/4)y^(16)\right)^(1/2) = \left(x^(1/4)\right)^(1/2)*\left(y^(16)\right)^(1/2)`

Then applying the second rule lets us say

`\left(x^(1/4)\right)^(1/2)*\left(y^(16)\right)^(1/2) = x^(1/4*1/2)*y^(16*1/2) = x^(1/8)y^(8)`

Therefore,

`\left(x^(1/4)y^(16)\right)^(1/2) = x^(1/8)y^(8)`

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In short, we just multiplied each exponent inside by the outer exponent 1/2.

So that explains why the exponents go from {1/4,16} to {1/8,8} for x and y in that exact order.