Question

Simplify:
$\frac{{\left(0.22\right)}^4\times {\left(0.222\right)}^3}{{\left(0.2\right)}^5\times {\left(0.2222\right)}^2}$

Answer 1

$\frac{{\left(0.22\right)}^4\times {\left(0.222\right)}^3}{{\left(0.2\right)}^5\times {\left(0.2222\right)}^2}$

$=\frac{{(1.1\times 0.2)}^4\times {(1.11\times 0.2)}^3}{{\left(0.2\right)}^5\times {(1.111\times 0.2)}^2}$

$=\frac{{\left(1.1\right)}^4\times {\left(0.2\right)}^4\times {\left(1.11\right)}^3\times {\left(0.2\right)}^3}{{\left(0.2\right)}^5\times {\left(1.111\right)}^2\times {\left(0.2\right)}^2}$

$=\frac{{\left(0.2\right)}^7\times {\left(1.11\right)}^3\times {\left(1.1\right)}^4}{{\left(0.2\right)}^7\times {\left(1.111\right)}^2}$

$=\frac{{\left(0.2\right)}^7\times {\left(1.11\right)}^3\times {\left(1.1\right)}^4}{{\left(0.2\right)}^7\times {(1.01\times 1.1)}^2}$

$=\frac{{\left(0.2\right)}^7\times {\left(1.11\right)}^3\times {\left(1.1\right)}^4}{{\left(0.2\right)}^7\times {\left(1.01\right)}^2\times {\left(1.1\right)}^2}$

$=\frac{{\left(0.2\right)}^{7-7}\times {\left(1.11\right)}^3\times {\left(1.1\right)}^{4-2}}{{\left(1.01\right)}^2}$

$=\frac{{\left(0.2\right)}^0\times {\left(1.11\right)}^3\times {\left(1.1\right)}^2}{{\left(1.01\right)}^2}$

$=\frac{{\left(1.11\right)}^3\times {\left(1.1\right)}^2}{{\left(1.01\right)}^2}$