The equivalent expression of the product expression [tex]\frac{m^3}{m^2 - 16} \div \frac{m^2 - 9}{m^4}[/tex] is [tex]\frac{m^7}{(m - 4)(m + 4)(m - 3)(m + 4)}[/tex]
The expression is given as:
[tex]\frac{m^3}{m^2 - 16} \div \frac{m^2 - 9}{m^4}[/tex]
Rewrite the expression as a product
[tex]\frac{m^3}{m^2 - 16} * \frac{m^4}{m^2 - 9}[/tex]
Evaluate the product
[tex]\frac{m^7}{(m^2 - 16)(m^2 - 9)}[/tex]
Rewrite the denominator as a difference of two squares
[tex]\frac{m^7}{(m - 4)(m + 4)(m - 3)(m + 4)}[/tex]
Hence, the equivalent expression of the product expression [tex]\frac{m^3}{m^2 - 16} \div \frac{m^2 - 9}{m^4}[/tex] is [tex]\frac{m^7}{(m - 4)(m + 4)(m - 3)(m + 4)}[/tex]
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