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What should come in place of the question mark (?) in the following questions?
Question 205
$$(4\times4\times4\times4\times4\times4)^{5}\times(4\times4\times4)^{8}\div(4)^{3}=(64)^?$$
Solution
The simplified expression equals $$(4\times4\times4\times4\times4\times4)^{5}\times(4\times4\times4)^{8}\div(4)^{3}= (4^6)^5 \times (4^3)^8 \div 4^3 = 4^{30} \times 4^{24} \div 4^3 = 4^{30+24-3} = 4^{51}$$
$$64 = 4^3$$
So, $$4^{51} = 4^{3 \times 17} = (4^3)^{17} = 64^{17}$$
Hence the correct answer is 17
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