[tex]__________________________[/tex]
[tex]\sf \large \frac{ (3 {x}^{2} {y}^{2} )(8 {x}^{3} y)}{(2 {x}^{2}y) ^{2} }[/tex]
First, use the power law to simplify the expression in the denominator where we have to raise every constants and variables to 2.
[tex]\sf \frac{ (3 {x}^{2} {y}^{2} )(8 {x}^{3} y)}{(2^{2} )( {x}^{2 \: \cdot \: 2} )(\: y^{1 \: \cdot \: 2} ) }[/tex]
[tex]\sf \frac{ (3 {x}^{2} {y}^{2} )(8 {x}^{3} y)}{(4 {x}^{4} y^{2} ) }[/tex]
Second, use the product law to multiply the two expressions in the numerator where in multiplying variables we just have to simply add the exponents and multiply the coefficient.
[tex]\sf \frac{(3 \: \cdot \: 8)(x^{2} \: \cdot \: {x}^{3})( {y}^{2} \: \cdot \: y) }{(4 {x}^{4} y^{2} ) }[/tex]
[tex]\sf \frac{24x^{5} {y}^{3} }{4 {x}^{4} y^{2} }[/tex]
Finally, use the quotient law to divide the two expressions where we to divide the constants and subtracting the exponents of the variables.
Always remember that there's an invisible exponent 1 in every variables. So instead of writing x¹ we can write it as x same goes for y¹ which is y.
[tex]\sf (\frac{24}{4} )( \frac{ {x}^{5} }{ {x}^{4} } )( \frac{ {y}^{3} }{ {y}^{2} } )[/tex]
[tex]\sf \boxed{ \sf 6xy}[/tex]
↬ Hence, simplify the expression will result to 6xy
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Answers & Comments
SIMPLIFYING ALGEBRAIC EXPRESSIONS
[tex]__________________________[/tex]
[tex]\sf \large \frac{ (3 {x}^{2} {y}^{2} )(8 {x}^{3} y)}{(2 {x}^{2}y) ^{2} }[/tex]
First, use the power law to simplify the expression in the denominator where we have to raise every constants and variables to 2.
[tex]\sf \frac{ (3 {x}^{2} {y}^{2} )(8 {x}^{3} y)}{(2^{2} )( {x}^{2 \: \cdot \: 2} )(\: y^{1 \: \cdot \: 2} ) }[/tex]
[tex]\sf \frac{ (3 {x}^{2} {y}^{2} )(8 {x}^{3} y)}{(4 {x}^{4} y^{2} ) }[/tex]
Second, use the product law to multiply the two expressions in the numerator where in multiplying variables we just have to simply add the exponents and multiply the coefficient.
[tex]\sf \frac{(3 \: \cdot \: 8)(x^{2} \: \cdot \: {x}^{3})( {y}^{2} \: \cdot \: y) }{(4 {x}^{4} y^{2} ) }[/tex]
[tex]\sf \frac{24x^{5} {y}^{3} }{4 {x}^{4} y^{2} }[/tex]
Finally, use the quotient law to divide the two expressions where we to divide the constants and subtracting the exponents of the variables.
Always remember that there's an invisible exponent 1 in every variables. So instead of writing x¹ we can write it as x same goes for y¹ which is y.
[tex]\sf (\frac{24}{4} )( \frac{ {x}^{5} }{ {x}^{4} } )( \frac{ {y}^{3} }{ {y}^{2} } )[/tex]
[tex]\sf \boxed{ \sf 6xy}[/tex]
↬ Hence, simplify the expression will result to 6xy