Evaluate. fourth root of 9 multiplied by square root of 9 over the fourth root of 9 to the power of 5

5 to the power of negative 1 over 6
5 to the power of 3 over 2
9
92

The answer is 1/3

To calculate this will use several rules:





The fourth root of 9 is 
Square root of 9 is 
The fourth root of 9 to the power of 5 is 

The fourth root of 9 multiplied by square root of 9 over the fourth root of 9 to the power of 5 is:
 

(1) Fourth root of 9 multiplied by square root of 9 over the fourth root of 9 to the power of 5.= 9^(1/4) * 9^(1/2) / (9^(1/4))^5, cancel 9^(1/4)= 9^(1/2) / (9^(1/4))^4= 9^(1/2) / 9= 3 / 9= 1/3

(2) Five to the power of negative 1 over 6= 5 ^ (-1/6)= (1/5)^(1/6)

(3) Five to the power of 3 over 2= 5 ^ (3/2)= sqrt(125)

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