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
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[tex]\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}}[/tex]
Alternatively, ...
[tex]\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}}[/tex]
