Question

Evaluate: $\frac{{28}^2\times {15}^3\times 625}{7^5\times {10}^8\times 6^3}$

Answer 1

Consider the given expression,

$\frac{{28}^2\times {15}^3\times 625}{7^5\times {10}^8\times 6^3}=\frac{{(7\times 4)}^2\times {(3\times 5)}^3\times 5^4}{7^5\times {(2\times 5)}^8\times {(3\times 2)}^3}$

$=\frac{7^2\times 4^2\times 3^3\times 5^3\times 5^4}{7^5\times 2^8\times 5^8\times 3^3\times 2^3}=\frac{7^2\times 5^{3+4}\times 3^3\times {\left(2^2\right)}^2}{7^2\times 5^8\times 3^3\times 2^{8+2}}$

$=\frac{7^2\times 5^7\times 3^3\times 2^4}{7^2\times 5^8\times 3^3\times 2^{10}}=\frac{1}{5\times 2^6}=\frac{1}{5\times 64}=\frac{1}{320}$

Hence, this is the answer.