Question

Which expression is equivalent to (4g3h2k4)3

Answer 1

Answer:

d) $8g^{6}h^{4} k^{12} - (h^{25} k^{15} )$

      $\frac{(4g^{3} h^{2}k^{4} )^{3} }{8g^{3}h^{2} } - (h^{5} k^{3} )^{5}$    $= 8g^{6}h^{4} k^{12} - (h^{25} k^{15} )$

Step-by-step explanation:

Explanation

Given expression

           =     $\frac{(4g^{3} h^{2}k^{4} )^{3} }{8g^{3}h^{2} } - (h^{5} k^{3} )^{5}$

By using

        (ab)ⁿ = aⁿbⁿ

         $\frac{a^{m} }{a^{n} } = a^{m-n}$

   =     $\frac{(4)^{3} g^{9} h^{6}k^{12} ) }{8g^{3}h^{2} } - (h^{5} k^{3} )^{5}$

After simplification , we get

  $= 8g^{9}g^{-3} h^{6} h^{-2} k^{12} - (h^{5} k^{3} )^{5}$

 $= 8g^{9-3}h^{6-2} k^{12} - (h^{5} k^{3} )^{5}$

$= 8g^{6}h^{4} k^{12} - (h^{25} k^{15} )$