Question

(0.75)^–2 = ______.

Options

• 0.375

• `9/16`

• `16/9`

• `1/5625`

Answer 1

(0.75)^–2 = `underlinebb(16/9)`.

Explanation:

We are asked to evaluate:

(0.75)^–2

Step 1: Express 0.75 as a fraction

`0.75 = 3/4`

Thus, the expression becomes:

`(3/4)^-2`

Step 2: Apply the negative exponent rule

Using the rule `a^-n = 1/a^n`, we can rewrite the expression as:

`(3/4)^-2 = 1/(3/4)^2`

Step 3: Square the fraction

`(3/4)^2 = 3^2/4^2 = 9/16`

Step 4: Final result

Now we have:

`1/(9/16) = 16/9`

The value of (0.75)^–2 is `16/9`.