Question

4/25^-1/2 how do u work this out help

Answer 1

9514 1404 393

Answer:

  5/2

Step-by-step explanation:

The rules of exponents apply.

  a^-b = 1/a^b

  (a^b)^c = a^(bc)

  a^(1/2) = √a

__

  $\left(\dfrac{4}{25}\right)^{-\frac{1}{2}}=4^{-\frac{1}{2}}(25^{-1})^{-\frac{1}{2}}=(2^2)^{-\frac{1}{2}}((5^2)^{-1})^{-\frac{1}{2}}=2^{-1}\cdot5^1=\boxed{\dfrac{5}{2}}$

Alternatively, ...

  $\left(\dfrac{4}{25}\right)^{-\frac{1}{2}}=\sqrt{\left(\dfrac{4}{25}\right)^{-1}}=\sqrt{\dfrac{25}{4}}=\dfrac{\sqrt{25}}{\sqrt{4}}=\boxed{\dfrac{5}{2}}$