Question

Simplify:
$\frac{{\left(0.0006\right)}^9}{{\left(0.015\right)}^{-4}}$

Answer 1

$\frac{{\left(0.0006\right)}^9}{{\left(0.015\right)}^{-4}}$

${=\left(0.0006\right)}^9\times {\left(0.015\right)}^4$

${=(6\times {10}^{-4})}^9\times {(15\times {10}^{-3})}^4$

$=(6{)}^9\times (10{)}^{-36}\times (15{)}^4\times ({10}^{-12})$

$=\frac{6^9\times {15}^4}{{10}^{36}\times {10}^{12}}$

$=\frac{(2\times 3{)}^9\times (5\times 3{)}^4}{(5\times 2{)}^{36}\times (5\times 2{)}^{12}}$

$=\frac{2^9\times 3^9\times 5^4\times 3^4}{5^{36}\times 2^{36}\times 5^{12}\times 2^{12}}$

$=\frac{3^{(9+4)}}{2^{(36+12-9)}\times 5^{(36+12-4)}}$

$=\frac{3^{13}}{2^{39}\times 5^{44}}$