Question

5^16 +125^5 is divisible by ​

Answer 1

$\red{ 5^{16} + 125^{5} } \\= 5^{16} + (5^{3})^{5} \\= 5^{ 1 + 15} + 5^{15}$

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$\underline { \blue { By \: Exponential\: Laws: }}$

$\pink { 1 . (a^{m})^{n} = a^{m \times n } }$

$\orange { 2. a^{m+n} = a^{m} \times a^{n} }$

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$= 5^{1} \times 5^{15} + 1 \times 5^{15} \\= 5^{15} (5 + 1 ) \\= 5^{15} \times 6 \\= 2 \times 3 \times 5^{15}$

Therefore.,

$\red{ 5^{16} + 125^{5} }$

$\green { \:is \: Divisible \:by \: 2, 3 , 6 \: and \: 5 }$

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