Jawaban:

[(216)^2/3 - (81)^3/4] / (243)^2/5

{\displaystyle \frac{(216)^{\frac{2}{3} } - (81)^{\frac{3}{4} }}{243^{\frac{2}{5}}}}

243

5

2

(216)

3

2

−(81)

4

3

= {\displaystyle \frac{(6^{3} )^{\frac{2}{3} } - (3^{4} )^{\frac{3}{4} }}{(3^{5}) ^{\frac{2}{5}}}}

(3

5

)

5

2

(6

3

)

3

2

−(3

4

)

4

3

= {\displaystyle \frac{6^{3 \times \frac{2}{3} } - 3^{4 \times \frac{3}{4} }}{3^{5 \times \frac{2}{5}}}}

3

5×

5

2

6

3×

3

2

−3

4×

4

3

= {\displaystyle \frac{6^{2} - 3^{3}}{3^{2}}}

3

2

6

2

−3

3

= {\displaystyle \frac{36 - 27}{9}}

9

36−27

= $$${\displaystyle \frac{9}{9}$}$$

= 1

II. (216)^2/3 - (81)^3/4 / (243)^2/5

{\displaystyle (216)^{\frac{2}{3} } - \frac{(81)^{\frac{3}{4} }}{(243)^{\frac{2}{5}}}}(216)

3

2

−

(243)

5

2

(81)

4

3

= {\displaystyle 6^{3 \times \frac{2}{3} } - \frac{3^{4 \times \frac{3}{4} }}{3^{5 \times \frac{2}{5}}}}6

3×

3

2

−

3

5×

5

2

3

4×

4

3

= {\displaystyle 6^{2} - \frac{3^{3} }{3^{2}}}6

2

−

3

2

3

3

= $$${\displaystle 36 - \frac{27}{9}$$

= 36 - 3

= 33