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Find:(i) \( \left(3^{2}\right)^{3} \times\left(2 \times 3^{5}\right)^{-2} \times(18)^{2} \) (ii) \( \frac{9^{2} \times 7^{3} \times 2^{5}}{84^{3}} \) (iii) \( \frac{2^{8} \times 2187}{3^{5} \times 32} \) |
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Answer» (i) (32)3 × (2 × 35)−2 × 182 = 36 x 2-2 x 3-10 x (-2 x 32)2 = 2-2 x 36-10 x 22 x 34 = 2-2 + 2 x 3-4 + 4 = 20 x 30 = 1 x 1 = 1 (ii) \(\cfrac{9^2\times7^3\times2^5}{84^3}\) = \(\cfrac{(3^2)^2\times7^3\times2^5}{(2^2\times3\times7)^3}\) = \(\cfrac{3^4\times7^3\times2^5}{2^6\times3^3\times7^3}\) = \(\cfrac{3^{4-3}}{2^{6-5}}\) = \(\cfrac32\) = 1.5 (iii) \(\cfrac{2^8\times2187}{3^5\times32}\) = \(\cfrac{2^8\times3^7}{3^5\times2^5}\) = 28-5 x 37-5 = 23 x 32 = 8 x 9 = 72 |
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