[tex]81^{\frac{1}{4} }[/tex] can be simplified into 3.
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 81 = 3 x 3 x 3 x 3 = [tex]3^{4}[/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]81^{\frac{1}{4} }[/tex] = [tex](3^{4} )^{\frac{1}{4} }[/tex]
Applying the law of indices mentioned above,
[tex](3^{m})^{n} = 3^{4 X\frac{1}{4} }[/tex]
= 3.
Thus, the
[tex]81^{\frac{1}{4} }[/tex] can be simplified into 3.
To learn more about laws of indices, refer to this link:
brainly.com/question/27432311
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