Answer:
[tex]8\sqrt2[/tex]
Second option is correct.
Step-by-step explanation:
We have been given the expression [tex](64)^{\frac{7}{12}}[/tex]
We can write the term 64 as [tex]64=2^6[/tex]
Thus, we have
[tex](2^6)^{\frac{7}{12}}[/tex]
Now, use the exponent law [tex](x^m)^n=x^{mn}[/tex]
[tex](2)^{6\cdot\frac{7}{12}}[/tex]
On simplifying, we get
[tex](2)^{\frac{7}{2}}[/tex]
This expression can be further simplified as
[tex]\sqrt{2^7}\\\\=\sqrt{2^6\cdot2}\\\\=2^3\sqrt{2}\\\\=8\sqrt2[/tex]
Second option is correct.
