Question

Simplify
$\frac{{15}^4\times {14}^2}{{21}^3\times {10}^3}$

Answer 1

The numerator is
${15}^4\times {14}^2={(3\times 5)}^4\times {(2\times 7)}^2=3^4\times 5^4\times 2^2\times 7^2$
Similarly the denominator is
${21}^3\times {10}^3={(7\times 3)}^3\times {(2\times 5)}^3=7^3\times 3^3\times 2^3\times 5^3$
The given expression is therefore
$\frac{3^4\times 5^4\times 2^2\times 7^2}{7^3\times 3^3\times 2^3\times 5^3}=3^{4-3}\times 5^{4-3}\times 2^{2-3}\times 7^{2-3}=\frac{3\times 5}{2\times 7}=\frac{15}{14}$