Question
Simplify:
$\frac{(16)^7\times(25)^5\times(81)^3}{(15)^7\times(24)^5\times(80)^3}$
$\frac{(16)^7\times(25)^5\times(81)^3}{(15)^7\times(24)^5\times(80)^3}$
✓
Answer
$\frac{(16)^7\times(25)^5\times(81)^3}{(15)^7\times(24)^5\times(80)^3}$
$=\frac{(16)^7\times(5^2)^5\times(3^4)^3}{(3\times5)^7\times(3\times8)^5\times(16\times5)^3}$
$=\frac{(16)^7\times(5^2)^5\times(3^4)^3}{3^7\times5^7\times3^5\times8^5\times16^3\times5^3}$
$=\frac{(16)^7\times(5^2)^5\times(3^4)^3}{3^{12}\times5^{10}\times8^5\times16^3}$
$=\frac{(16)^7}{8^5\times16^{3}}$
$=\frac{(16)^4}{8^5}$
$=\frac{(2\times8)^4}{8^5}$
$=\frac{2^4\times8^4}{8^5}$
$=\frac{2^4}{8}$
$=\frac{16}{8}$
$=2$
$=\frac{(16)^7\times(5^2)^5\times(3^4)^3}{(3\times5)^7\times(3\times8)^5\times(16\times5)^3}$
$=\frac{(16)^7\times(5^2)^5\times(3^4)^3}{3^7\times5^7\times3^5\times8^5\times16^3\times5^3}$
$=\frac{(16)^7\times(5^2)^5\times(3^4)^3}{3^{12}\times5^{10}\times8^5\times16^3}$
$=\frac{(16)^7}{8^5\times16^{3}}$
$=\frac{(16)^4}{8^5}$
$=\frac{(2\times8)^4}{8^5}$
$=\frac{2^4\times8^4}{8^5}$
$=\frac{2^4}{8}$
$=\frac{16}{8}$
$=2$
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