Question

Which expression is equivalent to ^4 square root x^10

Please help:/

Answer 1

Choice A is the correct answer. Nice work.

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One way to see this is to use the rule

$\sqrt[n]{x^m} = x^{m/n}$

and that leads to

$\sqrt[4]{x^{10}} = x^{10/4}$

which means we'll divide the 10 and 4 to get 10/4 = 2.5 = 2 remainder 2

The "2 remainder 2" part is all we care about really. The whole part 2 forms the exponent over the first x shown in choice A, while the "remainder 2" portion is the exponent over the x inside the root.

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Here's another example:

$\sqrt[4]{x^{27}} = x^{27/4} = x^6\sqrt[4]{x^3}$

Note how 27/4 = 6 remainder 3. We see that the whole part 6 is the first exponent of the result while 3 is the second exponent.