Question

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

92x 9 Superscript one-eighth x
StartRoot 9 EndRoot Superscript x RootIndex 5
StartRoot 9 EndRoot Superscript x

Answer 1

B

Explanation:

Answer 2

`{9}^ {(1)/(8)x}`

Explanation:

We want to find an equivalent expression for

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

To find an equivalent expression, we need to apply the following property of exponents:

`{a}^{ (m)/(n)}=( \sqrt[n]{ {a}} )^(m)`

We let a=9, n=4 and m=½x

Then :

`{9}^{ ( (1)/(2)x)/(4)}=( \sqrt[4]{ {9}} )^{ (1)/(2)x}`

Simplify the left hand side to get:

`{9}^ {(1)/(8)x} =( \sqrt[4]{ {9}} )^{ (1)/(2)x}`

Therefore the correct answer is:

`{9}^ {(1)/(8)x}`