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

(i) $$\frac{(2^5)^2× 7^3}{8^3 × 7}$$ = $$\frac{(2^{10}× 7^3}{(2^3)^3 × 7}$$
= $$\frac{(2^{10}× 7^3}{{2^9 × 7}$$ = $$2^{10-9}× 7^{3-1}$$ = $$2^1× 7^2$$ =2× 49 = 98
(ii) $$\frac{25×5^2× t^8}{10^3 ×t^4 }$$ = $$\frac{5^2×5^2× t^8}{2^3×5^3×t^4 }$$
= $$\frac{5^4× t^8}{2^3×5^3 ×t^4 }$$ = $$\frac{5^{4-3}× t^{8-4}}{2^3}$$ = $$\frac{5t^4}{2^3}$$
(iii) $$\frac{3^5×10^5× 25}{5^7 ×6^5 }$$= $$\frac{3^5×2^5×5^5× 5^2}{5^7 ×2^5×3^5 }$$
= $$\frac{3^5×5^7× 2^5}{5^7 ×2^5×3^5}$$ = 1