Question

What is the cube root of 27what is the factorization of 216x^12 - 64

Answer 1

Answers:

1) 27 is the same as multiplying three times three times three:

$(3)(3)(3)={3}^{3}=27$    (1)

Now, the cube root of 27 can be written as:

$\sqrt[3]{27}={(27)}^{\frac{1}{3}}$    (2)

Knowing the information given by (1) we can rewrite (2) as:

${({3}^{3})}^{\frac{1}{3}}$

Applying the rule of exponents with the same base, which in this case is 3:

${(3)}^{3(\frac{1}{3})}=3$

Finally:

$\sqrt[3]{27}=3$

2) We have the following expression:

$216{x}^{12}-64$

That can be factored by taking the common factor, which in this case is 8:

$8(27{x}^{12}-8)$

Then:

$216{x}^{12}-64=8(27{x}^{12}-8)$