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:

$9^{-\frac{5}{2}}$

Step 1: Factor the number

$9=3^2$

Therefore, the expression becomes:

$\Rightarrow(3^2)^{-\frac{5}{2}}$

Step 2: Apply the exponent rule given to be

$(x^a)^b=x^{a\times b}$

Therefore, we have:

$\Rightarrow(3^2)^{-\frac{5}{2}}=3^{2\times-\frac{5}{2}}=3^{-5}$

Step 3: Apply the exponent rule given to be

$x^{-a}=\frac{1}{x^a}$

Therefore, the expression becomes:

$3^{-5}=\frac{1}{3^5}$

Step 4: Calculate

$3^5=243$

Therefore, we have

$\frac{1}{3^5}=\frac{1}{243}$

ANSWER

$9^{-\frac{5}{2}}=\frac{1}{243}$