9-3-161-2-6-2- 1-27-4-3

9^ 3×16^126^ 2× (127)^ 43 =1729× 4 × 36 × 81 =16 ...

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Complex Numbers

9-3×161/2/6-2...

Question

Find the value of $9^{- 3} \times \frac{16^{\frac{1}{2}}}{6^{- 2}} \times (\frac{1}{27})^{- \frac{4}{3}}$

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Solution

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(9)^{- 3} \times \frac{16^{\frac{1}{4}}}{6^{- 2}} \times {(\frac{1}{27})}^{- \frac{4}{3}}

\frac{(64)^{- \frac{1}{6}} \times (216)^{- \frac{1}{3}} \times (81)^{\frac{1}{4}}}{(512)^{- \frac{1}{3}} \times (16)^{\frac{1}{4}} \times (9)^{- \frac{1}{2}}}

(i) (1^{3} + 2^{3} + 3^{3})^{\frac{1}{2}} (i i) {(\frac{3}{5})}^{4} {(\frac{8}{5})}^{- 12} {(\frac{32}{5})}^{6} (i i i) {(\frac{1}{27})}^{\frac{- 2}{3}} (i v) {⎡ ⎣ {((625)^{- \frac{1}{2}})}^{\frac{- 1}{4}} ⎤ ⎦}^{2} (v) \frac{9^{\frac{1}{3}} \times 27^{- \frac{1}{2}}}{3^{\frac{1}{6}} \times 3^{\frac{- 2}{3}}}

(v i) 64^{\frac{- 1}{3}} [64^{\frac{1}{3}} - 64^{\frac{2}{3}}] (v i i) \frac{8^{\frac{1}{3}} \times 16^{\frac{1}{3}}}{32^{\frac{- 1}{3}}}

\frac{(64)^{- 1 / 6} \times (216)^{- 1 / 3} \times (81)^{1 / 4}}{(512)^{12} \times (16)^{1 / 4} \times (9)^{- 1 / 2}}

Find all the cube root of $- 4 \sqrt{2} - 4 \sqrt{2} i$

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