Question

simplify

1.(-5y^5) (3y^7) / 10y^12

2. x^2m / x^m

Answer 1

1 ) :
$\dfrac{( - 5y {}^{5})(3y {}^{7} ) }{10{}y^{12} }$



Solving numerator that is $( - 5y {}^{5})(3y {}^{7} )$



$( - 5y {}^{5})(3y {}^{7} )$

$( - 5)(y {}^{5})(3)(y {}^{7} )$

$( - 5)(3)(y {}^{5})( {y}^{7} )$

$-15(y^{5+7}$

$-15y^{12}$




Now,$\dfrac{( - 5y {}^{5})(3y {}^{7} ) }{10{}y^{12} }= \dfrac{-15 \times y^{12}}{y^{12}}$



→ - 15




( ii ) :

$\dfrac{ {x}^{2m} }{x {}^{m} }$


From the properties of exponents,


${x}^{2m - m} \\ \\ {x}^{m(2 - 1)} \\ \\ {x}^{m(1)} \\ \\ {x}^{m}$