Question

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

Answer 1

ans by aaabanti :

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

8

1

x

Step-by-step explanation:

We want to find an equivalent expression for

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

4

9

)

2

1

x

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

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

n

m

=(

n

a

)

m

We let a=9, n=4 and m=½x

Then :

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

4

2

1

x

=(

4

9

)

2

1

x

Simplify the left hand side to get:

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

8

1

x

=(

4

9

)

2

1

x

Therefore the correct answer is:

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

8

1

x