Answer
$4$
Work Step by Step
Using the laws of exponents, the given expression, $
\dfrac{-52y^{-2}}{-13y^{-2}}
,$ is equivalent to
\begin{array}{l}\require{cancel}
(-52\div(-13))y^{-2-(-2)}
\\\\=
4y^{-2+2}
\\\\=
4y^{0}
\\\\=
4(1)
\\\\=
4
.\end{array}
For more complicated problems, it is helpful to remember that you can flip the location of numbers with negative exponents. In other words, you can move numbers with a negative exponent that are in the numerator to the denominator, and you can move numbers with a negative exponent in the denominator to the numerator.
