Question

`(0.008)^(-2//3)` = ______.

Options

• 0.2

• 0.4

• 5

• 25

Answer 1

`(0.008)^(-2//3)` = 25.

Explanation:

We are asked to evaluate:

`(0.008)^(-2/3)`

Step 1: Express 0.008 as a power of 10

First, we can express 0.008 as:

0.008 = 8 × 10^–3

Now, the expression becomes:

`(8 xx 10^-3)^(-2/3)`

Step 2: Apply the exponent rule

Using the exponent rule (ab)ⁿ = aⁿ × bⁿ, we can separate the terms:

`(8 xx 10^-3)^(-2/3) = 8^(-2/3) xx (10^-3)^(-2/3)`

Step 3: Simplify each part

1. Simplify `8^(-2/3)`:

Recall that 8 = 2³, so:

`8^(-2/3) = (2^3)^(-2/3)`

= 2^–2

= `1/2^2`

= `1/4`

2. Simplify `(10^-3)^(-2/3)`:

Using the exponent rule (a^m)ⁿ = a^{m × n}, we get:

`(10^-3)^(-2/3) = 10^((-3) xx (-2/3))`

= 10²

= 100

Step 4: Combine the results

Now multiply the two simplified terms:

= `1/4 xx 100`

= `100/4`

= 25

The value of `(0.008)^(-2/3) = 25`.