Question

Evaluate fourth root of 9 multiplied by square root of 9 over the fourth root of 9 to the power of 5 . (5 points) Question options:

1) 9 to the power of negative 1 over 2
2) 9 to the power of negative 1 over 4
3) 9
4) 92]

Answer 1

1) 9 to the power of negative 1 over 2

Explanation:

I took the test

Answer 2

Option 1) 9 to the power of negative 1 over 2

Explanation:

We have to evaluate the following expression:

`(9)^{(1)/(4)}* \frac{√(9)}{(9^{(1)/(4)})^5}`

Exponential properties:

`(x^a)^b = x^(ab)\\\\(x^a)/(x^b) = x^(a-b)\\\\x^a* x^b = x^(a+b)`

Evaluating the expression, we get,

`(9)^{(1)/(4)}* \frac{√(9)}{(9^{(1)/(4)})^5}\\\\(9)^{(1)/(4)}* \frac{9^{(1)/(2)}}{(9^{(5)/(4)})}\\\\=(9)^{(1)/(4)}* (9)^{(1)/(2)-(5)/(4)}\\\\=(9)^{(1)/(4)}* (9)^{(-3)/(4)}\\\\=(9)^{(1)/(4)+(-3)/(4)}\\\\=(9)^{(-1)/(2)}`

Thus, the correct answer is

Option 1) 9 to the power of negative 1 over 2