which expression is equivalent to $(4h^{7}k^{2})^{4}$?\n$16h^{11}k^{6}$\n$16h^{28}k^{8}$\n$256h^{11}k^{6}$\n$…

which expression is equivalent to $(4h^{7}k^{2})^{4}$?\n$16h^{11}k^{6}$\n$16h^{28}k^{8}$\n$256h^{11}k^{6}$\n$256h^{28}k^{8}$

which expression is equivalent to $(4h^{7}k^{2})^{4}$?\n$16h^{11}k^{6}$\n$16h^{28}k^{8}$\n$256h^{11}k^{6}$\n$256h^{28}k^{8}$

Answer

Answer:

D. $256h^{28}k^{8}$

Explanation:

Step1: Apply power - of - a - product rule

$(4h^{7}k^{2})^{4}=4^{4}\times(h^{7})^{4}\times(k^{2})^{4}$

Step2: Calculate $4^{4}$

$4^{4}=4\times4\times4\times4 = 256$

Step3: Apply power - of - a - power rule for $h$

$(h^{7})^{4}=h^{7\times4}=h^{28}$

Step4: Apply power - of - a - power rule for $k$

$(k^{2})^{4}=k^{2\times4}=k^{8}$

Step5: Combine the results

$4^{4}\times(h^{7})^{4}\times(k^{2})^{4}=256h^{28}k^{8}$