Which is equivalent to \sqrt[4]{9} ^{(1)/(2)x } A: 9^(2x) B:9^{(1)/(8)x } C:√(9)^(x) D:\sqrt[6]{9} ^(x) ANSWER IS B: :9^{(1)/(8)x }

Question

Which is equivalent to
`\sqrt[4]{9} ^{(1)/(2)x }`

A:
`9^(2x)`
B:
`9^{(1)/(8)x }`
C:
`√(9)^(x)`
D:
`\sqrt[6]{9} ^(x)`



ANSWER IS B: :
`9^{(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