Question

Evaluate:

`125^((-2)/3) xx 9^(1/2)`

Answer 1

Let’s evaluate the expression step by step:

We are asked to evaluate:

`125^(((-2)/3)) xx 9^(1/2)`

Step 1: Simplify `125^(((-2)/3))`

First, express 125 as a power of 5:

125 = 5³

Now, using the property of exponents (a^m)ⁿ = a^{m × n}, we get

`125^(((-2)/3)) = (5^3)^((-2)/3)`

= `5^(3 xx (-2)/3)`

= 5^–2

Thus:

`125^(((-2)/5)) = 1/5^2 = 1/25`

Step 2: Simplify `9^(1/2)`

We know that 9 = 3², so:

`9^(1/2) = (3^2)^(1/2)`

= `3^(2 xx 1/2)`

= 3

Step 3: Multiply the two results

Now, multiply the results from Step 1 and Step 2:

`1/25 xx 3 = 3/25`

The value of the expression is `3/25`