Answer:
[tex]6r^3[/tex]
Step-by-step explanation:
[tex]\left(216r^9\right)^{\frac{1}{3}}[/tex]
Apply exponent rule: [tex]\left(a\times \:b\right)^n=a^nb^n[/tex]
[tex]\longmapsto[/tex] [tex]\left(216r^9\right)^{\frac{1}{3}}=216^{\frac{1}{3}}\left(r^9\right)^{\frac{1}{3}}[/tex]
[tex]\longmapsto216^{\frac{1}{3}}\left(r^9\right)^{\frac{1}{3}}[/tex]
[tex]216^{\frac{1}{3}}[/tex]
Factor 216 = 6³
[tex]\longmapsto \left(6^3\right)^{\frac{1}{3}}[/tex]
Apply exponent rule: [tex]\left(a^b\right)^c=a^{bc},\:\quad \:a\ge 0[/tex]
[tex]\longmapsto[/tex] [tex]\left(6^3\right)^{\frac{1}{3}}=6^{3\cdot \frac{1}{3}}[/tex]
[tex]\longmapsto 6^{3\cdot \frac{1}{3}}[/tex]
[tex]\longmapsto3\times \frac{1}{3}=1[/tex]
[tex]\longmapsto6^1[/tex]
[tex]\longmapsto6[/tex]
[tex]6\left(r^9\right)^{\frac{1}{3}}[/tex]
Apply exponent rule: [tex]\left(a^b\right)^c=a^{bc}[/tex]
[tex]\longmapsto\left(r^9\right)^{\frac{1}{3}}=r^{9\cdot \frac{1}{3}}[/tex]
[tex]\longmapsto6r^{9\cdot \frac{1}{3}}[/tex]
[tex]\longmapsto9\times\frac{1}{3} =3[/tex]
[tex]\longmapsto6r^3[/tex]
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