1.
[tex]8 {x}^{3} \times \frac{3}{4} {x}^{5} = (8 \times \frac{3}{4} )( {x}^{3} \times {x}^{5} ) \\ = (8 \times \frac{3}{4} )( {x}^{3 + 5} ) \\ = 6 {x}^{8} [/tex]
2.
[tex]2 {x}^{3} \times 4 \sqrt{x} = (2 \times 4)( {x}^{3} \times \sqrt{x} ) \\ = (2 \times 4)( {x}^{3} \times {x}^{ \frac{1}{2} } ) \\ = (2 \times 4)( {x}^{3 + \frac{1}{2} } ) \\ = 8 {x}^{ \frac{7}{2} } = 8 \sqrt[2]{ {x}^{7} } [/tex]
3.
[tex] \frac{6 {x}^{4} }{2 {x}^{7} } = ( \frac{6}{2} )( \frac{ {x}^{4} }{ {x}^{7} } ) \\ = ( \frac{6}{2} )( {x}^{4 -7} ) \\ = 3 {x}^{ - 3} = \frac{3}{ {x}^{3} } [/tex]
4.
[tex] \frac{4x}{ \sqrt[3]{ {x}^{2} } } = \frac{4x}{ {x}^{ \frac{2}{3} } } \\ = ( \frac{4}{1} )( \frac{ {x}^{1} }{ {x}^{ \frac{2}{3} } } ) \\ = ( \frac{4}{1} )( {x}^{1 - \frac{2}{3} } ) \\ = 4 {x}^{ \frac{1}{3} } = 4 \sqrt[3]{x} [/tex]
5.
[tex] ({ {2x}^{3} })^{2} = 2 {x}^{3} \times 2 {x}^{3} \\ = (2 \times 2)( {x}^{3} \times {x}^{3} ) \\ = (2 \times 2)( {x}^{3 + 3} ) \\ = 4 {x}^{6} [/tex]
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