7.92*10^-2/(4*10^-3)^2

asked by guest
on Nov 15, 2024 at 4:35 am



You asked:

Evaluate the expression: \(\frac{7.92 \cdot {10}^{-2}}{{\left( 4 \cdot {10}^{-3} \right)}^{2}}\)

MathBot Answer:

\[\frac{7.92 \cdot {10}^{-2}}{{\left( 4 \cdot {10}^{-3} \right)}^{2}} = 4950\]

\[\begin{aligned}\frac{7.92 \cdot {10}^{-2}}{{\left( 4 \cdot {10}^{-3} \right)}^{2}}& = \left(7 + \frac{92}{100}\right) \cdot \frac{1}{10^{2}} \cdot \frac{1}{\left(4 \cdot \frac{1}{10^{3}}\right)^{2}}\\& = \left(7 + \frac{23}{25}\right) \cdot \frac{1}{10^{2}} \cdot \frac{1}{\left(4 \cdot \frac{1}{10^{3}}\right)^{2}}\\& = \frac{198}{25} \cdot \frac{1}{10^{2}} \cdot \frac{1}{\left(4 \cdot \frac{1}{10^{3}}\right)^{2}}\\& = \frac{198}{25} \cdot \frac{1}{100} \cdot \frac{1}{\left(4 \cdot \frac{1}{10^{3}}\right)^{2}}\\& = \frac{198}{25} \cdot \frac{1}{100} \cdot \frac{1}{\left(\frac{4}{1000}\right)^{2}}\\& = \frac{198}{25} \cdot \frac{1}{100} \cdot \frac{1}{\left(\frac{1}{250}\right)^{2}}\\& = \frac{198}{25} \cdot \frac{1}{100} \cdot \frac{1}{\frac{1}{62500}}\\& = \frac{198}{25} \cdot 625\\& = 4950\end{aligned}\]

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