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

Question

asked Apr 16, 2020 90.0k views

2 Answers

Cancerian · Answer 1 · 2020-04-20T06:50:34+0000

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:

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

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

${({3}^(3))}^{(1)/(3)}$

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

${(3)}^{3((1)/(3))}=3$

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:

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