Respuesta :
[tex]125. 125^{\frac{1}{3} }[/tex] can be simplified into 625.
Prime factorization is the process of breaking down a number into its prime factors. Multiplying these prime numbers gives back the original number.
Prime factorization of 125 = 5 x 5 x 5 = [tex]5^{3}[/tex]
According to the law of indices, if a term with a power is raised to a power, then the powers are multiplied together.
i.e., [tex](x^{m})^{n} = x^{mn}[/tex]
Another law of indices says that if two terms having same base are multiplied together, then their indices are added.
i.e., [tex]a^{m} X a^{n} = a^{m+n}[/tex]
According to the given condition,
[tex]125. 125^{\frac{1}{3} }[/tex] = [tex]5^{3} .( 5^{3} )^{\frac{1}{3} }[/tex]
Applying the laws of indices mentioned above,
[tex]125. 125^{\frac{1}{3} }[/tex] = [tex]5^{3} .( 5^{3 X} ^{\frac{1}{3} })[/tex]
= [tex]5^{3} .( 5 )[/tex] = [tex]5^{3 + 1}[/tex]
= [tex]5^{4} = 625.[/tex]
Thus, [tex]125. 125^{\frac{1}{3} }[/tex] can be simplified into 625.
To learn more about laws of indices, refer to this link:
brainly.com/question/27432311
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