Question

Simplifique a expressão:

Resposta: 3000

Answer 1

$A=\dfrac{5^{x+3}-5^{x+1}}{5^{x-2}}\\ \\ A=\dfrac{5^{x-2+5}-5^{x-2+3}}{5^{x-2}}\\ \\ A=\dfrac{5^{x-2}\cdot 5^{5}-5^{x-2}\cdot 5^{3}}{5^{x-2}}\\ \\ A=\dfrac{5^{x-2}\cdot\left(5^{5}-5^{3} \right )}{5^{x-2}}\\ \\ A=5^{5}-5^{3}\\ \\ A=5^{3+2}-5^{3}\\ \\ A=5^{3}\cdot 5^{2}-5^{3}\\ \\ A=5^{3}\cdot \left(5^{2}-1 \right )\\ \\ A=125\cdot \left(25-1 \right )\\ \\ A=125 \cdot 24\\ \\ \boxed{A=3\,000}$