Question

se √625= 5 qual o valor de a

Answer 1

$\textrm{Algumas propriedades envolvendo}\\ \textrm{radicia\c{c}\~ao e potencia\c{c}\~ao:}\\\\ \mathrm{\sqrt[\mathrm{n}]{\mathrm{a}}=a^{\frac{1}{n}}\ \ \|\ \ \big(a^n\big)^m=a^{n.m}}\\\\ \mathrm{\sqrt[\mathrm{a}]{625}=5\ \to\ 625^{\frac{1}{a}}=5}\\ \mathrm{\big(5^4\big)^{\frac{1}{a}}=5\ \to\ 5^{\frac{4}{a}}=5^1}\\\\ \textrm{Comparando os expoentes:}\\\\ \mathrm{\frac{4}{a}=1\ \to\ \boxed{\mathbf{a=4}}}$