Respuesta:
1) 5² = 25
2) 2³ = 8
3) [tex]5^{4}[/tex] = 625
4) [tex]2^{1}[/tex] =2
Explicación paso a paso:
Uso de las propiedades de los radicales y potencias.
Recordemos:
[tex]\sqrt[a]{\sqrt[b]{x} }[/tex] = [tex]\sqrt[ab]{x}[/tex]
[tex]\sqrt[n]{x}^{y} } = x^{y/n}[/tex]
Aplicando las propiedades:
[tex]\sqrt[3]{\sqrt{\sqrt{5^{24} } } }[/tex] = [tex]\sqrt[3*2*2]{5^{24} }[/tex] = [tex]\sqrt[12]{5^{24} }[/tex] = [tex]5^{24/12}[/tex] = 5² = 25
[tex]\sqrt[2]{\sqrt[5]{2^{30} } }[/tex] = [tex]\sqrt[2*5]{2^{30} }[/tex] = [tex]\sqrt[10]{2^{30} }[/tex] = [tex]2^{30/10}[/tex] = 2³ = 8
[tex]\sqrt[3]{5^{12} }[/tex] = [tex]5^{12/3}[/tex] = [tex]5^{4}[/tex] = 625
[tex]\sqrt[2]{\sqrt[3]{64} }[/tex] = [tex]\sqrt[2*3]{64}[/tex] = [tex]\sqrt[6]{64}[/tex] = 2
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Respuesta:
1) 5² = 25
2) 2³ = 8
3) [tex]5^{4}[/tex] = 625
4) [tex]2^{1}[/tex] =2
Explicación paso a paso:
Uso de las propiedades de los radicales y potencias.
Recordemos:
[tex]\sqrt[a]{\sqrt[b]{x} }[/tex] = [tex]\sqrt[ab]{x}[/tex]
[tex]\sqrt[n]{x}^{y} } = x^{y/n}[/tex]
Aplicando las propiedades:
[tex]\sqrt[3]{\sqrt{\sqrt{5^{24} } } }[/tex] = [tex]\sqrt[3*2*2]{5^{24} }[/tex] = [tex]\sqrt[12]{5^{24} }[/tex] = [tex]5^{24/12}[/tex] = 5² = 25
[tex]\sqrt[2]{\sqrt[5]{2^{30} } }[/tex] = [tex]\sqrt[2*5]{2^{30} }[/tex] = [tex]\sqrt[10]{2^{30} }[/tex] = [tex]2^{30/10}[/tex] = 2³ = 8
[tex]\sqrt[3]{5^{12} }[/tex] = [tex]5^{12/3}[/tex] = [tex]5^{4}[/tex] = 625
[tex]\sqrt[2]{\sqrt[3]{64} }[/tex] = [tex]\sqrt[2*3]{64}[/tex] = [tex]\sqrt[6]{64}[/tex] = 2