Question

Simplify:
(i) $\frac{(2^5)^2×7^3}{8^3×7}$ (ii) $\frac{2^5×5^2×t^8}{10^3×t^4}$ (iii) $\frac{3^5×10^5×25}{5^7×6^5}$

Answer 1

(i)$\frac{(2^5)^2×7^3}{8^3×7}$
= $\frac{(2^5)^2×7^3}{{(2×2×2)}^3×7}$ [(am)n=amn]
= $\frac{2^{10}×7^3}{(2^3)^3×7}$ [(am)n=amn]
= 21×72=2×7×7=98

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(ii)$\frac{2^5×5^2×t^8}{10^3×t^4}$
= $\frac{5\times5×5^2×t^8}{{(5\times 2)}^3×t^4}$ (a×b)m=(am×bm)
= $\frac{5^{1+1+2}×t^8}{5^3×2^3×t^4}$ (am×an=am+n)
= $\frac{5^{4-3}×t^{8-4}}{2^3}$ (am÷an=am-n)
= $\frac{5^1×t^4}{2×2×2}$
= $\frac{5t^4}{8}$

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(iii)$\frac{3^5×10^5×25}{5^7×6^5}$
= $\frac{3^5×2^5×5^5×5^2}{5^7×2^5×3^5}$ (a×b)m=(am×bm)
= $\frac{3^2×2^5×5^{5+2}}{5^7×2^5×3^5}$ (am×an=am+n)
= $\frac{3^5×2^5×5^7}{5^7×2^5×3^5}$
= 35-5×25-5×57-7 (am÷an=am-n)
= 30×20×50
= 1×1×1
= 1