Resposta:
1. [tex]x^6[/tex]
2. [tex]8[/tex]
3. [tex]5^{30}[/tex]
4. [tex]25[/tex]
5. [tex]252[/tex]
Explicação passo a passo:
1. [tex]\frac{x^4x^6x^8}{x^2x^4x^6}=\frac{x^6x^8}{x^2x^6}=\frac{x^8}{x^2}=x^6[/tex]
2. [tex]\left(2^6\div \:2^4\right)+2^2=4+2^2=4+4=8[/tex]
3. [tex]\frac{\left(5^2\cdot \:5^4\right)^6}{\left(\frac{5^{10}}{5^8}\right)^3}=\frac{\left(5^2\cdot \:5^4\right)^6}{15625}=\frac{5^{12}\cdot \:5^{24}}{15625}=\frac{5^{12}\cdot \:5^{24}}{5^6}=5^6\cdot \:5^{24}=5^{30}[/tex]
4. [tex]5^2-3^2+500^0-\left(-2\right)^3=25-3^2+500^0-\left(-2\right)^3=25-9+500^0-\left(-2\right)^3=25-9+1-\left(-2\right)^3=25-9+1-\left(-8\right)=25[/tex]
5. [tex]\frac{a}{b}=\frac{2^7\cdot \:3^8\cdot \:7}{2^5\cdot \:3^6}=\frac{2^2\cdot \:3^8\cdot \:7}{3^6}=2^2\cdot \:3^2\cdot \:7=252[/tex]
