Question

Simplify:
$\frac{{\left(16\right)}^7\times {\left(25\right)}^5\times {\left(81\right)}^3}{{\left(15\right)}^7\times {\left(24\right)}^5\times {80}^3}$

Answer 1

Now,

$\frac{{\left(16\right)}^7\times {\left(25\right)}^5\times {\left(81\right)}^3}{{\left(15\right)}^7\times {\left(24\right)}^5\times {80}^3}$

$=\frac{{\left(2^4\right)}^7\times {\left(5^2\right)}^5\times {\left(3^4\right)}^3}{{(3\times 5)}^7\times {(2^3\times 3)}^5\times {2^{12}\times 5}^3}$

$=\frac{{\left(2\right)}^{28}\times {\left(5\right)}^{10}\times {\left(3\right)}^{12}}{{\left(3\right)}^7\times 5^7\times {\left(2\right)}^{15}\times 3^5\times 2^{12}\times 5^3}$

$=\frac{{\left(2\right)}^{28}\times {\left(5\right)}^{10}\times {\left(3\right)}^{12}}{{\left(3\right)}^{12}\times {\left(2\right)}^{27}\times 5^{10}}$

$=2$.