Question

Is $\frac{{\left({10}^4\right)}^3}{5^{13}}$ an integer? Justify your answer.

Answer 1

Consider, $\frac{{\left({10}^4\right)}^3}{5^{13}}$

$=\frac{{10}^{12}}{5^{(12+1)}}$

$=\frac{{(5\times 2)}^{12}}{5^{12}\times 5^1}$

$=\frac{5^{12}\times 2^{12}}{5^{12}\times 5^1}$

$=\frac{2^{12}}{5}$

$=\frac{4096}{5}$

$=819.2$

Hence, it is not an integer as it contains decimal.