Answer:
2
Step-by-step explanation:
Given expression:
[tex]\large\text{$\dfrac{216^{\frac13}}{27^{\frac13}}$}[/tex]
Part 1
To simplify the numerator, rewrite 216 as 6³:
[tex]\large\text{$216^{\frac13}=(6^3)^{\frac13}$}[/tex]
Now, apply the power of a power exponent rule:
[tex]\large\text{$(6^3)^{\frac13}=6^{\left(3 \times \frac13\right)}=6^1=6$}[/tex]
Therefore, the numerator simplifies to 6.
[tex]\dotfill[/tex]
Part 2
To simplify the denominator, rewrite 27 as 3³:
[tex]\large\text{$27^{\frac13}=(3^3)^{\frac13}$}[/tex]
Now, apply the power of a power exponent rule:
[tex]\large\text{$(3^3)^{\frac13}=3^{\left(3 \times \frac13\right)}=3^1=3$}[/tex]
Therefore, the denominator simplifies to 3.
[tex]\dotfill[/tex]
Part 3
As the numerator simplifies to 6 and the denominator simplifies to 3, then:
[tex]\large\text{$\dfrac{216^{\frac13}}{27^{\frac13}}=\dfrac{6}{3}=2$}[/tex]
