Answer
$\dfrac{1}{125}$
Work Step by Step
Recall the basic exponent property (pg. 360):
$(a^m)^n=a^{mn}$
Thus, the given expression is equivalent to:
$=25^{-3\left(\frac{1}{2}\right)}\\
=\left(25^{\frac{1}{2}}\right)^{-3}$
Recall that $\sqrt[n]{x}=x^{\frac{1}{n}}$.
Thus, the expression above is equivalent to:
$=(\sqrt{25})^{-3}$
Since $5^2=25$, then the expression above simplifies to:
$=(5)^{-3}$
Recall the basic exponent property (pg. 383):
$a^{-m}=\frac{1}{a^m}$
Applying this, we get:
$(5)^{-3}=\dfrac{1}{(5)^{3}}=\dfrac{1}{125}$
