Question

Which is equivalent to ula1" title="\sqrt[4]{9} ^{\frac{1}{2}x }" alt="\sqrt[4]{9} ^{\frac{1}{2}x }" align="absmiddle" class="latex-formula">
A: $9^{2x}$
B:$9^{\frac{1}{8}x }$
C:$\sqrt{9}^{x}$
D:$\sqrt[6]{9} ^{x}$



ANSWER IS B: :$9^{\frac{1}{8}x }$

Answer 1

For this case we have that by definition of properties of powers and roots, it is fulfilled that:

$\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}$

So:

$\sqrt [4] {9 ^ {\frac {1} {2} x}} = 9 ^ {\frac {\frac {1} {2}} {4} x} = 9 ^ {\frac {1} {8} x}$

So, we have to:

$\sqrt [4] {9 ^ {\frac {1} {2} x}} = 9 ^ {\frac {1} {8} x}$

Answer:

$9 ^ {\frac {1} {8} x}$

Option B