Evaluate

One must know some properties of exponent to solve this.

${ \left( -\cfrac { 1 }{ 125 } \right) }^{ { -2 }/{ 3 } }={ \left( -125 \right) }^{ { 2 }/{ 3 } }={ \left[ { \left( -125 \right) }^{ \cfrac { 1 }{ 3 } } \right] }^{ 2 }={ \left[ { \left( -{ 5 }^{ 3 } \right) }^{ \cfrac { 1 }{ 3 } } \right] }^{ 2 }=(-5 )^{ 2 }=25$

$\left(-\dfrac{1}{125} \right)^{-\frac{2}{3}} = \left(- 5^{-3} \right)^{-\frac{2}{3}} = (-5)^{(-3)\left(-\frac{2}{3}\right)} = (-5)^2 = \boxed{25}$

$(-\frac {1}{125})^{\frac {-2}{3}}$

$-\frac {1}{125}$ can be written as $(-5)^{-3}$

So $(-\frac {1}{125})^{\frac {-2}{3}}$ becomes $((-5)^{-3})^{\frac {-2}{3}}$

Since $(n^x)^y = n^{xy}$ we can write it as

$(-5)^2 = 25$

So the answer is $25$

According to the question, (-1/5)^3*-2/3

According to the law of exponents, (a^m)^n= a^mn

Therefore, The expression is(-1/5)^-2 because (-2/3*3=-2)

=-5^2 because [(1/a)]^-m=a^m

Answer= 25

${ {\left(-\frac{1}{125}\right)}^{ -\frac{2}{3} } ={ {\left(\left({-5}\right)^{ -3}\right)}^{ -\frac{2}{3} } } = \left({-5}\right)^{2} = \underline{25} }$

-1/125)^-2/3 = (-1/125)^-1(2/3) (-125)^2/3 (-5)^2 25

(-1/125)^-2/3=(-125)^2/3=cubic root of 125^2 =cubic root of 5^6 =5 ^(6/3)=5^2=25