Answer:
✒Exponential Expressions
[tex]\huge\sf\color {violet}\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull[/tex]
Simplify:
[tex] \sf \: a. \: ( - 3 {x}^{4} y{}^{5} ) {}^{3} [/tex]
[tex] \sf \:b. \: ( - 7 {xy}^{4} )( - 2 {x}^{5} {y}^{6} )[/tex]
[tex] \sf \: c. \: \frac{ - 35 {x}^{2} {y}^{2} }{5 {x}^{6} {y}^{ - 8} } [/tex]
[tex] \sf \: d. \: ( \frac{ {4x}^{2} }{y} ) {}^{ - 3} [/tex]
[tex]\huge\sf\color {violet}\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull[/tex]
Solution:
[tex] \sf \: a. \: ( - 3 {x}^{4} {y}^{5} ) {}^{3} = ( - 3) {}^{3} {( {x}^{4} )}^{3} (y {}^{5} ) {}^{3} \\ \sf= ( - 3) {}^{3} x {}^{4 \times 3} y {}^{5 \times 3} \\ \sf = - 27 {x}^{12} {y}^{15} [/tex]
[tex]\huge\sf\color {violet}\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull[/tex]
[tex]\sf \:b. \: ( - 7 {xy}^{4} )( - 2 {x}^{5} {y}^{6} ) = ( - 7)( - 2) {xx}^{5}y {}^{4} {y}^{6} \\ \sf \: = 14 {x}^{1 + 5} {y}^{4 + 6} \\ \sf \: = 14 {x}^{6} {y}^{10} [/tex]
[tex]\huge\sf\color {violet}\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull[/tex]
[tex] \sf \: c. \: \frac{ - 35 {x}^{2} {y}^{2} }{5 {x}^{6} {y}^{ - 8} } = ( \frac{ - 35}{5} )( \frac{ {x}^{2} }{ {x}^{6} } )( \frac{ {y}^{4} }{ {y}^{ - 8} } ) \\ \sf \: - 7 {x}^{2 - 6} {y}^{4} ( - 8) \\ \sf \: = - 7x {}^{ - 4} y {}^{12} \\ \sf \: = \frac{ - 7 {y}^{12} }{ {x}^{4} } [/tex]
[tex]\huge\sf\color {violet}\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull[/tex]
[tex] \sf \: d. \: ( \frac{ {4x}^{2} }{y} ) {}^{ - 3} = \frac{ {4}^{ - 3 } ({x}^{2}) {}^{ - 3} }{ {y}^{ - 3} } \\ \sf \: = \frac{{4}^{ - 3 } {x}^{ - 6} }{ {y}^{ - 3} } \\ \sf \: = \frac{ {y}^{3} }{ {4}^{3} {x}^{6} } \\ \sf \: = \frac{ {y}^{3} }{64 {x}^{6} } [/tex]
[tex]\huge\sf\color {violet}\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull\bull[/tex]
