Question

Which of the following is equal to the square root of the cube root of 5? 5 to the power of 1 over 3 5 to the power of 1 over 6 5 to the power of 2 over 3 5 to the power of 3 over 2

Answer 1

Answer

5 to the power of 1 over 6

or as an expression:  $5^{\frac{1}{6} }$

Explanation

First we are going to express our statement as an algebraic expression:

square root of the cube root of 5 = $\sqrt{\sqrt[3]{5} }$

Next, we are using laws of radicals to simplify our expression:

Law of radicals: $\sqrt[m]{\sqrt[n]{a} } =\sqrt[mn]{a}$

We can infer from our expression that n=2, m=3, and a=5, so lets replace the values:

$\sqrt{\sqrt[3]{5} }=\sqrt[(2)(3)]{5} =\sqrt[6]{5}$

Now, to express the radical as exponent, we are going to use another law of radicals:

Law of radicals: $\sqrt[n]{a} =a^{\frac{1}{n} }$

Just like before, we can infer for our expression that n=6 and a=5, so let's replace the values:

$\sqrt[6]{5} =5^{\frac{1}{6} }$

And in words:

square root of the cube root of 5 is equal to 5 to the power of 1 over 6

Answer 2

5 to the power of 1/6. Use simple exponent rules.... square root= X^(1/2) and cube root = X^(1/3)