Elementary Algebra

$13$
Using the laws of exponents, the given expression, $\dfrac{-91y^{-3}}{-7y^{-3}} ,$ is equivalent to \begin{array}{l}\require{cancel} (-91\div(-7))y^{-3-(-3)} \\\\= 13y^{-3+3} \\\\= 13y^{0} \\\\= 13(1) \\\\= 13 .\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.