Question

7B%5Cfrac%7B5%7D%7B2%7D%20%7D%29%20%282k%5E%7B%5Cfrac%7B3%7D%7B4%7D%20%7D%29" id="TexFormula1" title="(3h^{\frac{5}{2} })( 2k^{\frac{3}{4} })(3h^{\frac{5}{2} }) (2k^{\frac{3}{4} })" alt="(3h^{\frac{5}{2} })( 2k^{\frac{3}{4} })(3h^{\frac{5}{2} }) (2k^{\frac{3}{4} })" align="absmiddle" class="latex-formula">
Please Show Your Work

Answer 1

Answer:

$486h^{5}k\sqrt{2k}$

Step-by-step explanation:

We have to simplify the expression $(3h^{\frac{5}{2}})(2k^{\frac{3}{4}})(3h^{\frac{5}{2}})(2k^{\frac{3}{4}})$

Now,

$(3h^{\frac{5}{2}})(2k^{\frac{3}{4}})(3h^{\frac{5}{2}})(2k^{\frac{3}{4}})$

= $(3^{\frac{5}{2}}\times 3^{\frac{5}{2}})\times (2^{\frac{3}{4}} \times 2^{\frac{3}{4}}) \times (h^{\frac{5}{2}}\times h^{\frac{5}{2}})\times (k^{\frac{3}{4}} \times k^{\frac{3}{4}})$

{As the terms are in product form, so we can treat them separately}

= $3^{(\frac{5}{2} + \frac{5}{2})} \times 2^{(\frac{3}{4} + \frac{3}{4})} \times h^{(\frac{5}{2} + \frac{5}{2})} \times k^{(\frac{3}{4} + \frac{3}{4})}$

{Since, we know that $a^{b} \times a^{c} = a^{b + c}$}

= $3^{5} \times 2^{\frac{3}{2}} \times h^{5} \times k^{\frac{3}{2}}$

= $243 \times 2\sqrt{2} \times h^{5}\times k^{\frac{3}{2} }$

= $486\sqrt{2} \times h^{5} \times k\sqrt{k}$

= $486h^{5}k\sqrt{2k}$ (Answer)