[(9 × 10⁹) * (2.0 × 10⁻⁶ ) * (-3.0 × 10⁻⁶ )] / (0.02 )²

asked by guest
on Nov 13, 2024 at 9:54 pm



You asked:

Evaluate the expression: \(\frac{9 \cdot {10}^{9} \cdot 2.0 \cdot {10}^{-6} \cdot -3.0 \cdot {10}^{-6}}{{0.02}^{2}}\)

MathBot Answer:

\[\frac{9 \cdot {10}^{9} \cdot 2.0 \cdot {10}^{-6} \cdot -3.0 \cdot {10}^{-6}}{{0.02}^{2}} = -135\]

\[\begin{aligned}\frac{9 \cdot {10}^{9} \cdot 2.0 \cdot {10}^{-6} \cdot -3.0 \cdot {10}^{-6}}{{0.02}^{2}}& = 9 \cdot 10^{9} \cdot 2 \cdot \frac{1}{10^{6}} \cdot -3 \cdot \frac{1}{10^{6}} \cdot \frac{1}{\left(\frac{2}{100}\right)^{2}}\\& = 9 \cdot 1000000000 \cdot 2 \cdot \frac{1}{10^{6}} \cdot -3 \cdot \frac{1}{10^{6}} \cdot \frac{1}{\left(\frac{2}{100}\right)^{2}}\\& = 9 \cdot 1000000000 \cdot \frac{2}{1000000} \cdot -3 \cdot \frac{1}{10^{6}} \cdot \frac{1}{\left(\frac{2}{100}\right)^{2}}\\& = 9 \cdot 1000000000 \cdot \frac{2}{1000000} \cdot \frac{-3}{1000000} \cdot \frac{1}{\left(\frac{2}{100}\right)^{2}}\\& = 9 \cdot 1000000000 \cdot \frac{2}{1000000} \cdot \frac{-3}{1000000} \cdot \frac{1}{\left(\frac{1}{50}\right)^{2}}\\& = 9 \cdot 1000000000 \cdot \frac{2}{1000000} \cdot \frac{-3}{1000000} \cdot \frac{1}{\frac{1}{2500}}\\& = 9 \cdot 1000000000 \cdot \frac{2}{1000000} \cdot \frac{-3}{400}\\& = 9000000000 \cdot \frac{2}{1000000} \cdot \frac{-3}{400}\\& = \frac{18000000000}{1000000} \cdot \frac{-3}{400}\\& = 18000 \cdot \frac{-3}{400}\\& = \frac{-54000}{400}\\& = -135\end{aligned}\]

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