## Intermediate Algebra (12th Edition)

$\dfrac{y^{7}}{x^{13}z^{2}}$
Use the laws of exponents to simplify the given expression, $\dfrac{x^{-6}y^3z^{-1}}{x^7y^{-4}z} .$ Using the Quotient Rule of the laws of exponents which states that $\dfrac{x^m}{x^n}=x^{m-n},$ the quotient of the expression above is \begin{array}{l}\require{cancel} x^{-6-7}y^{3-(-4)}z^{-1-1} \\\\= x^{-6-7}y^{3+4}z^{-1-1} \\\\= x^{-13}y^{7}z^{-2} .\end{array} Using the Negative Exponent Rule of the laws of exponents which states that $x^{-m}=\dfrac{1}{x^m}$ or $\dfrac{1}{x^{-m}}=x^m,$ the expression above is equivalent to \begin{array}{l}\require{cancel} \dfrac{y^{7}}{x^{13}z^{2}} .\end{array}