Question

Simplify:
$\frac{6^8\times 5^3}{{10}^3\times 3^4}$

Answer 1

$\frac{6^8\times 5^3}{{10}^3\times 3^4}$

$=\frac{{(3\times 2)}^8\times 5^3}{{(2\times 5)}^3\times 3^4}$

$=\frac{3^8\times 2^8\times 5^3}{2^3\times 5^3\times 3^4}$ ......(using${\left(xy\right)}^n=x^n.y^n$)

$=3^{(8-4)}\times 2^{(8-3)}\times 5^{(3-3)}$ ......(using $\frac{x^n}{x^m}=x^{n-m}$)

$=3^4\times 2^{\left(5\right)}\times 5^0$

$=81\times 32\times 1$

$=2592$