Question

What is the most simplified expression that is equivalent to (-4x)^3*(27x^18)^1/3

Answer 1

$\bf (-4x)^3\cdot \left( 27x^{18} \right)^{\frac{1}{3}}\implies (-2^2x)^3\cdot \left( 3^3x^{18} \right)^{\frac{1}{3}}\implies \left( (-2)^{2\cdot 3}x^3 \right)\left(3^{\frac{3}{3}}x^{\frac{18}{3}} \right) \\\\\\ (-2)^6x^3\cdot 3^1x^6\implies (-2)^6\cdot 3^1x^3\cdot x^6\implies -192x^{3+6}\implies -192x^9$