6. $(7a^{5}b^{6})^{4}=$

Explanation:

Step1: Apply power - of - a - product rule

$(7a^{5}b^{6})^{4}=7^{4}\times(a^{5})^{4}\times(b^{6})^{4}$

Step2: Calculate $7^{4}$

$7^{4}=7\times7\times7\times7 = 2401$

Step3: Apply power - of - a - power rule for $a$ and $b$ terms

$(a^{5})^{4}=a^{5\times4}=a^{20}$ and $(b^{6})^{4}=b^{6\times4}=b^{24}$

Step4: Combine the results

$7^{4}\times(a^{5})^{4}\times(b^{6})^{4}=2401a^{20}b^{24}$

Answer:

$2401a^{20}b^{24}$