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

Answer:

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

Step-by-step explanation:

We have to evaluate the following expression:

$(9)^{\frac{1}{4}}\times \dfrac{\sqrt{9}}{(9^{\frac{1}{4}})^5}$

Exponential properties:

$(x^a)^b = x^{ab}\\\\\dfrac{x^a}{x^b} = x^{a-b}\\\\x^a\times x^b = x^{a+b}$

Evaluating the expression, we get,

$(9)^{\frac{1}{4}}\times \dfrac{\sqrt{9}}{(9^{\frac{1}{4}})^5}\\\\(9)^{\frac{1}{4}}\times \dfrac{9^{\frac{1}{2}}}{(9^{\frac{5}{4}})}\\\\=(9)^{\frac{1}{4}}\times (9)^{\frac{1}{2}-\frac{5}{4}}\\\\=(9)^{\frac{1}{4}}\times (9)^{\frac{-3}{4}}\\\\=(9)^{\frac{1}{4}+\frac{-3}{4}}\\\\=(9)^{\frac{-1}{2}}$

Thus, the correct answer is

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

Answer 2

Answer:

1) 9 to the power of negative 1 over 2

Step-by-step explanation:

I took the test