Example

3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b

Question

$$4 { A }^{ 6 } { B }^{ 3 } -10 { A }^{ 4 } { B }^{ 6- } 8 { A }^{ 9 } { B }^{ 9 }$$

Answer

$$4*A^6*B^3-80*A^13*B^(6-+9)$$

Solution


Take out the constants.
\[4{A}^{6}{B}^{3}-(10\times 8){A}^{4}{A}^{9}{B}^{6-}{B}^{9}\]
Simplify  \(10\times 8\)  to  \(80\).
\[4{A}^{6}{B}^{3}-80{A}^{4}{A}^{9}{B}^{6-}{B}^{9}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[4{A}^{6}{B}^{3}-80{A}^{4+9}{B}^{6-+9}\]
Simplify  \(4+9\)  to  \(13\).
\[4{A}^{6}{B}^{3}-80{A}^{13}{B}^{6-+9}\]
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