Simplify \(2\times {10}^{-9}\times 8\times {10}^{-9}\) to \(16\times {10}^{-9}\times {10}^{-9}\).
\[9\times {10}^{9}\times \frac{16\times {10}^{-9}\times {10}^{-9}}{{(5\times {10}^{-3})}^{2}}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[9\times {10}^{9}\times \frac{16\times {10}^{-18}}{{(5\times {10}^{-3})}^{2}}\]
Simplify \({10}^{9}\) to \(1000000000\).
\[9\times 1000000000\times \frac{16\times {10}^{-18}}{{(5\times {10}^{-3})}^{2}}\]
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[9\times 1000000000\times \frac{16\times {10}^{-18}}{{5}^{2}{({10}^{-3})}^{2}}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[9\times 1000000000\times \frac{16\times {10}^{-18}}{{5}^{2}{(\frac{1}{{10}^{3}})}^{2}}\]
Simplify \({10}^{3}\) to \(1000\).
\[9\times 1000000000\times \frac{16\times {10}^{-18}}{{5}^{2}{(\frac{1}{1000})}^{2}}\]
Simplify \({5}^{2}\) to \(25\).
\[9\times 1000000000\times \frac{16\times {10}^{-18}}{25{(\frac{1}{1000})}^{2}}\]
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[9\times 1000000000\times \frac{16\times {10}^{-18}}{25\times \frac{1}{{1000}^{2}}}\]
Simplify \({1000}^{2}\) to \(1000000\).
\[9\times 1000000000\times \frac{16\times {10}^{-18}}{25\times \frac{1}{1000000}}\]
Simplify \(25\times \frac{1}{1000000}\) to \(\frac{25}{1000000}\).
\[9\times 1000000000\times \frac{16\times {10}^{-18}}{\frac{25}{1000000}}\]
Simplify \(\frac{25}{1000000}\) to \(\frac{1}{40000}\).
\[9\times 1000000000\times \frac{16\times {10}^{-18}}{\frac{1}{40000}}\]
Invert and multiply.
\[9\times 1000000000\times 16\times {10}^{-18}\times 40000\]
Simplify \(9\times 1000000000\) to \(9000000000\).
\[9000000000\times 16\times {10}^{-18}\times 40000\]
Simplify \(9000000000\times 16\) to \(144000000000\).
\[144000000000\times {10}^{-18}\times 40000\]
Simplify.
\[5.76\times {10}^{15}\times {10}^{-18}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[5.76\times {10}^{-3}\]
Decimal Form: 0.00576
5.76*10^-3
