Simplify the expression Assume that all variables represent

Simplify the expression. Assume that all variables represent nonzero real numbers. StartFraction left parenthesis 4 n cubed q Superscript 4 right parenthesis squared left parenthesis 8 n cubed q right parenthesis Superscript negative 2 Over left parenthesis negative 3 nq Superscript 7 right parenthesis Superscript negative 1 Baseline left parenthesis 4 n cubed q Superscript 7 right parenthesis cubed EndFraction (4n3q4)2 (8n3q)2 (3nq7)1 (4n3q7)3

Solution

(4n3q4)2 (8n3q)-2 (-3nq7)-1 (4n3q7)3
= (4n^3*q^4)^2 (8n^3*q)^-2 (-3n*q^7)^-1 (4n^3*q^7)^3
= (16*n^6*q^8) (n^-6*q^-2/64) (-n^-1*q^-7/3) (64*n^9*q^21)
= (16/3)*n^8*q^20