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Answer:
Step-by-step explanation:
1. The cube root is found by dividing the exponents by 3.
[tex]\sqrt[3]{27a^{12}}=(3^3\cdot a^{12})^{\frac{1}{3}}=3^{\frac{3}{3}}\cdot a^{\frac{12}{3}}=\boxed{3a^4}\qquad\text{matches d}[/tex]
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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 ...
[tex]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}[/tex]
