Calculate: 2vw^{-3} * 9w^3 * 2u^7v^{-5}u^{-3}

Expression: $216={\left( \frac{ 1 }{ 6 } \right)}^{x+3}$

Write the number in exponential form with the base of $6$

${6}^{3}={\left( \frac{ 1 }{ 6 } \right)}^{x+3}$

Express with a positive exponent using ${\left( \frac{ 1 }{ a } \right)}^{-n}={a}^{n}$

${6}^{3}={6}^{-x-3}$

Since the bases are the same, set the exponents equal

$3=-x-3$

Move the variable to the left-hand side and change its sign

$3+x=-3$

Move the constant to the right-hand side and change its sign

$x=-3-3$

Calculate the difference

$x=-6$