Answered

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Expresa como potencia de exponente fraccionario o como raíz, según corresponda.

a) [tex]\sqrt{a^4} =[/tex]

Sagot :

GinnyAnswer
Para resolver la expresión [tex]\(\sqrt{a^4}\)[/tex], seguimos los siguientes pasos:

1. Identificamos el radical y la potencia dentro de la raíz cuadrada.

La expresión dada es [tex]\(\sqrt{a^4}\)[/tex].

2. Recordamos que la raíz cuadrada de una base elevada a un exponente se puede expresar como:

[tex]\[ \sqrt{x^n} = x^{\frac{n}{2}} \][/tex]

En este caso, [tex]\(x = a\)[/tex] y [tex]\(n = 4\)[/tex].

3. Aplicamos la propiedad mencionada:

[tex]\[ \sqrt{a^4} = a^{\frac{4}{2}} \][/tex]

4. Simplificamos el exponente dividiendo [tex]\(4\)[/tex] entre [tex]\(2\)[/tex]:

[tex]\[ a^{\frac{4}{2}} = a^2 \][/tex]

Por lo tanto, la expresión [tex]\(\sqrt{a^4}\)[/tex] puede simplificarse y escribirse como [tex]\(a^2\)[/tex]. Esto nos da el resultado final:

[tex]\[ \sqrt{a^4} = a^2 \][/tex]
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