How do you simplify (2x^2y^-5)(-6x^-5y^3)(1/3x^-1y^6) and write it using only positive exponents?

May 31, 2017

$\frac{- 4 {y}^{4}}{{x}^{4}}$

Explanation:

Use the following 3 Laws of Exponents to simplify the expression:

${a}^{- m} = \frac{1}{a} ^ m$

$\left({a}^{m}\right) \left({a}^{n}\right) = {a}^{m + n}$

${a}^{m} / {a}^{n} = {a}^{m - n}$

$\left(2 {x}^{2}\right) \left(\frac{1}{y} ^ 5\right) \left(- 6 {y}^{3}\right) \left(\frac{1}{x} ^ 5\right) \left(\frac{1}{3} {y}^{6}\right) \left(\frac{1}{x}\right)$

$\frac{- 12 {x}^{2} {y}^{3} {y}^{6}}{3 {y}^{5} {x}^{5} x}$

$\frac{- 4 {x}^{2} {y}^{9}}{{y}^{5} {x}^{6}}$

$\frac{- 4 {y}^{4}}{{x}^{4}}$