To answer this question, we can proceed as follows:
1. We have that the expression is:
[tex]4^2(10)^{-2}[/tex]
We know from the negative exponent rule that:
[tex]x^{-m}=\frac{1}{x^m}[/tex]
Then we can apply this rule to the original expression as follows:
[tex]\begin{gathered} 4^2(10)^{-2}\Rightarrow(10)^{-2}=\frac{1}{10^2} \\ \frac{4^2}{10^2} \end{gathered}[/tex]
Now, we also know that the quotient to a power rule is given by:
[tex](\frac{x}{y})^m=\frac{x^m}{y^m}[/tex]
Therefore, we can say that:
[tex]\frac{4^2}{10^2}=(\frac{4}{10})^2[/tex]
Now, we can divide both the numerator and the denominator by 2 as follows (the fraction remains the same):
[tex]\begin{gathered} (\frac{\frac{4}{2}}{\frac{10}{2}})^2=(\frac{2}{5})^2 \\ \end{gathered}[/tex]
And finally, applying the same rule as before - quotient to a power rule - we have:
[tex](\frac{2}{5})^2=\frac{2^2}{5^2}=\frac{4}{25}=0.16[/tex]
In summary, therefore, the expression:
[tex]4^2(10)^{-2}[/tex]
Can be simplified as (in square millimeters):
[tex]\frac{4}{25}=0.16[/tex]
