[tex]100^{\frac{-3}{ 2} }[/tex] can be simplified into 0.001.
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 100 = 5 x 5 x 2 x 2 = [tex]10^{2}[/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]
According to the given condition,
∴ [tex]100^{\frac{-3}{2} }[/tex] = [tex](10^{2})^{\frac{-3}{2} }[/tex]
Applying the law of indices mentioned above,
[tex]100^{\frac{-3}{2} }[/tex] = [tex](10^{2 X}^{\frac{-3}{2} })[/tex]
= [tex]10^{-3}[/tex] = 0.001.
Thus, [tex]100^{\frac{-3}{2} }[/tex] can be simplified into 0.001.
To learn more about laws of indices, refer to this link:
brainly.com/question/27432311
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