Answers:
1) 27 is the same as multiplying three times three times three:
[tex](3)(3)(3)={3}^{3}=27[/tex] (1)
Now, the cube root of 27 can be written as:
[tex]\sqrt[3]{27}={(27)}^{\frac{1}{3}}[/tex] (2)
Knowing the information given by (1) we can rewrite (2) as:
[tex]{({3}^{3})}^{\frac{1}{3}}[/tex]
Applying the rule of exponents with the same base, which in this case is 3:
[tex]{(3)}^{3(\frac{1}{3})}=3[/tex]
Finally:
[tex]\sqrt[3]{27}=3[/tex]
2) We have the following expression:
[tex]216{x}^{12}-64[/tex]
That can be factored by taking the common factor, which in this case is 8:
[tex]8(27{x}^{12}-8)[/tex]
Then:
[tex]216{x}^{12}-64=8(27{x}^{12}-8)[/tex]
