Question

Find the value of √(625)^-2

Answer 1

$\rm{ {\sqrt{{(625)}^{- 2}}}}$

${\boxed{\rm{ {(a)}^{- m} = {\dfrac{1}{(a)^m}} }}}$

$\rm{\Rightarrow {\sqrt{ {\dfrac{1}{(625)^2}} }} }$

$\tt{REMOVING \ THE \ SQUARE \ ROOT.}$

$\rm{\Rightarrow {[{\dfrac{1}{(625)^2}}]}^{ {\frac{1}{2}}} }$

$\rm\red{\Rightarrow {\dfrac{1}{625}}}$

Answer 2

Answer:

√(625)^-2

We know any number raised to a negative power is the the positive power of its reciprocal:  a^-3 = 1/a^3

∴ √(1/625)²

=> 1/625 = 0.0016