Question

PLZ HELPPP!! Both answers plz

Answer 1

9514 1404 393

Answer:

1. d
2. d

Explanation:

1. The cube root is found by dividing the exponents by 3.

`\sqrt[3]{27a^(12)}=(3^3\cdot a^(12))^{(1)/(3)}=3^{(3)/(3)}\cdot a^{(12)/(3)}=\boxed{3a^4}\qquad\text{matches d}`

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The factoring of the difference of cubes is ...

a³ -b³ = (a -b)(a² +ab +b²)

Here, we have a=r^9 and b=s^10, so the factorization is ...

`r^(27)-s^(30)= (r^9-s^(10))(r^(9\cdot2)+r^9s^(10)+s^(10\cdot2))\\\\=\boxed{(r^9-s^(10))(r^(18)+r^9s^(10)+s^(20))} \qquad\text{matches d}`