Question

Matemática, potência. Como faço pra somar essas potências

Answer 1

$\displaystyle \sf \frac{10^{\frac{n}{2}}\cdot(10^{m-1}+10^{m+1})}{10^{m}\cdot(10^{\frac{n}{2}}+10^{2+\frac{n}{2}})} \\\\\\ \frac{10^{\frac{n}{2}}\cdot(10^{m}\cdot 10^{-1}+10^{m}\cdot 10^1)}{10^{m}\cdot(10^{\frac{n}{2}}+10^{\frac{n}{2}}\cdot 10^2)} \\\\\\ \text{numerador : colocando o }10^{m}\ \text{em evid{\^e}ncia}\\\\ \text{denominador : }colocando \ o }\ 10^{\frac{n}{2}}\ \text{em evid{\^e}ncia} \\\\\\\ \frac{10^{\frac{n}{2}}\cdot 10^{m}\cdot (10^{-1}+10^{1})}{10^{m}\cdot 10^{\frac{n}{2}}\cdot (1+10^2)}$

$\displaystyle \sf \frac{10^{-1}+10^1}{1+10^2} \\\\\\ \frac{0,1+10}{1+100} \\\\\\ \frac{10,1}{101} \\\\\\ \frac{101\cdot 10^{-1}}{101} \\\\\\ \huge\boxed{\sf 10^{-1}}\checkmark$

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