Factor out the common term \(2\).
\[\frac{2(4a+{b}^{8}{c}^{2})}{8{a}^{2}}-\frac{6{b}^{7}}{16{a}^{7}{c}^{9}}\]
Simplify \(\frac{2(4a+{b}^{8}{c}^{2})}{8{a}^{2}}\) to \(\frac{4a+{b}^{8}{c}^{2}}{4{a}^{2}}\).
\[\frac{4a+{b}^{8}{c}^{2}}{4{a}^{2}}-\frac{6{b}^{7}}{16{a}^{7}{c}^{9}}\]
Simplify \(\frac{6{b}^{7}}{16{a}^{7}{c}^{9}}\) to \(\frac{3{b}^{7}}{8{a}^{7}{c}^{9}}\).
\[\frac{4a+{b}^{8}{c}^{2}}{4{a}^{2}}-\frac{3{b}^{7}}{8{a}^{7}{c}^{9}}\]
Rewrite the expression with a common denominator.
\[\frac{(4a+{b}^{8}{c}^{2}){a}^{5}\times 8{c}^{9}-3{b}^{7}\times 4}{4{a}^{7}\times 8{c}^{9}}\]
Regroup terms.
\[\frac{8{a}^{5}{c}^{9}(4a+{b}^{8}{c}^{2})-3{b}^{7}\times 4}{4{a}^{7}\times 8{c}^{9}}\]
Simplify \(3{b}^{7}\times 4\) to \(12{b}^{7}\).
\[\frac{8{a}^{5}{c}^{9}(4a+{b}^{8}{c}^{2})-12{b}^{7}}{4{a}^{7}\times 8{c}^{9}}\]
Factor out the common term \(4\).
\[\frac{4(2{a}^{5}{c}^{9}(4a+{b}^{8}{c}^{2})-3{b}^{7})}{4{a}^{7}\times 8{c}^{9}}\]
Simplify \(4{a}^{7}\times 8{c}^{9}\) to \(32{a}^{7}{c}^{9}\).
\[\frac{4(2{a}^{5}{c}^{9}(4a+{b}^{8}{c}^{2})-3{b}^{7})}{32{a}^{7}{c}^{9}}\]
Simplify.
\[\frac{2{a}^{5}{c}^{9}(4a+{b}^{8}{c}^{2})-3{b}^{7}}{8{a}^{7}{c}^{9}}\]
(2*a^5*c^9*(4*a+b^8*c^2)-3*b^7)/(8*a^7*c^9)
