Question

`(16/625)^(-1/4)` = ______.

Options

• `4/25`

• `2/5`

• `25/4`

• `5/2`

Answer 1

`(16/625)^(-1/4)` = `underlinebb(5/2)`.

Explanation:

We are asked to evaluate:

`(16/625)^(-1/4)`

Step 1: Simplify the expression

We can rewrite the expression using the property of negative exponents:

`a^-n = 1/a^n`

So, the expression becomes:

`(16/625)^(-1/4) = 1/(16/625)^(1/4)`

Step 2: Simplify `(16/625)^(1/4)`

Now, simplify the fourth root of `16/625 = (4/25)^2`

Taking the fourth root of both the numerator and the denominator:

`(4/25)^(1/2) = 4^(1/2)/25^(1/2) = 2/5`

Step 3: Final step

Now, the expression becomes:

`1/(2/5) = 5/2`