Question

I need a better step by step on how to get the answer instead of just “calculate 9 to the power of -5/2 and get 1/243

Answer 1

The question ask to evaluate the expression:

`9^{-(5)/(2)}`

Step 1: Factor the number

`9=3^2`

Therefore, the expression becomes:

`\Rightarrow(3^2)^{-(5)/(2)}`

Step 2: Apply the exponent rule given to be

`(x^a)^b=x^(a* b)`

Therefore, we have:

`\Rightarrow(3^2)^{-(5)/(2)}=3^{2*-(5)/(2)}=3^(-5)`

Step 3: Apply the exponent rule given to be

`x^(-a)=(1)/(x^a)`

Therefore, the expression becomes:

`3^(-5)=(1)/(3^5)`

Step 4: Calculate

`3^5=243`

Therefore, we have

`(1)/(3^5)=(1)/(243)`

ANSWER

`9^{-(5)/(2)}=(1)/(243)`