Respuesta :
[tex]\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \qquad \qquad
\sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}\\\\
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\left( 16^{\frac{3}{2}} \right)^{\frac{1}{2}}\implies 16^{\frac{3}{2}\cdot \frac{1}{2}}\implies 16^{\frac{3}{4}}\qquad \boxed{16=2^4}\qquad (2^4)^{\frac{3}{4}}\implies 2^{4\cdot \frac{3}{4}}
\\\\\\
2^3\implies 8[/tex]
Answer:
Option B is correct that is 8.
Step-by-step explanation:
Given Expression : [tex](16^{\frac{3}{2}})^{\frac{1}{2}}[/tex]
We use a law of exponent here to simplify it,
[tex](x^a)^b=x^{ab}[/tex]
Consider,
[tex](16^{\frac{3}{2}})^{\frac{1}{2}}[/tex]
[tex]=16^{\frac{3}{2}\times\frac{1}{2}}[/tex]
[tex]=16^{\frac{3}{4}}[/tex]
[tex]=(2^4)^{\frac{3}{4}}[/tex]
[tex]=2^{4\times\frac{3}{4}}[/tex]
[tex]=2^3[/tex]
[tex]=8[/tex]
Therefore, Option B is correct that is 8.
