Question

Which is equivalent to RootIndex 4 StartRoot 9 EndRoot Superscript one-half x?

Answer 1

Answer:

Option B; the second one; 9^1/8

Step-by-step explanation:

Answer 2

The expression for which you want to find an equivalent form is:

• ${(\sqrt[4]{9})}^{\frac{1}{2}x}$

Answer:

Here there are 3 equivalent expressions:

• ${(\sqrt[4]{3^2})}^{\frac{1}{2}x}$

• $(\sqrt{3})^{\frac{1}{2}x}$

• $(\sqrt[4]{3} )^x$

Explanation:

There are many equivalent forms that you can find, so I will show some of the most important.

The first step that you should do is to put the radicand number (the number inside the root, i.e. 3) as a product of its prime factors. Thus the first equivalent expression is:

• ${(\sqrt[4]{3^2})}^{\frac{1}{2}x}$

Now you can simplify the root index, 4, with the exponent of the radicand, 2, an you get a new equivalent:

• ${(\sqrt[4]{3^2})}^{\frac{1}{2}x}=(\sqrt{3})^{\frac{1}{2}x}$

Another equivalent form is obtained if you convert the 1/2 index (before the x) into a root index:

• $(\sqrt{3})^{\frac{1}{2}x}=(\sqrt{\sqrt{3}})^x=(\sqrt[4]{3} )^x$

The main properties used to find those equivalent expressions are:

• $a^{\frac{1}{n}}=\sqrt[n]{a}$

And:

• ${(a^{\frac{1}{n}})^m=a^{\frac{m}{n}}= \sqrt[n]{a^m}$