Answer:
[tex]486h^{5}k\sqrt{2k}[/tex]
Step-by-step explanation:
We have to simplify the expression [tex](3h^{\frac{5}{2}})(2k^{\frac{3}{4}})(3h^{\frac{5}{2}})(2k^{\frac{3}{4}})[/tex]
Now,
[tex](3h^{\frac{5}{2}})(2k^{\frac{3}{4}})(3h^{\frac{5}{2}})(2k^{\frac{3}{4}})[/tex]
= [tex](3^{\frac{5}{2}}\times 3^{\frac{5}{2}})\times (2^{\frac{3}{4}} \times 2^{\frac{3}{4}}) \times (h^{\frac{5}{2}}\times h^{\frac{5}{2}})\times (k^{\frac{3}{4}} \times k^{\frac{3}{4}})[/tex]
{As the terms are in product form, so we can treat them separately}
= [tex]3^{(\frac{5}{2} + \frac{5}{2})} \times 2^{(\frac{3}{4} + \frac{3}{4})} \times h^{(\frac{5}{2} + \frac{5}{2})} \times k^{(\frac{3}{4} + \frac{3}{4})}[/tex]
{Since, we know that [tex]a^{b} \times a^{c} = a^{b + c}[/tex]}
= [tex]3^{5} \times 2^{\frac{3}{2}} \times h^{5} \times k^{\frac{3}{2}}[/tex]
= [tex]243 \times 2\sqrt{2} \times h^{5}\times k^{\frac{3}{2} }[/tex]
= [tex]486\sqrt{2} \times h^{5} \times k\sqrt{k}[/tex]
= [tex]486h^{5}k\sqrt{2k}[/tex] (Answer)
