Question

At the 2005 World Exposition in Aichi, Japan, tiny mu-chips were embedded in the admissions tickets to prevent counterfeiting. The mu-chip was developed by Hitachi in 2003.

Answer 1

To answer this question, we can proceed as follows:

1. We have that the expression is:

`4^2(10)^(-2)`

We know from the negative exponent rule that:

`x^(-m)=(1)/(x^m)`

Then we can apply this rule to the original expression as follows:

`\begin{gathered} 4^2(10)^(-2)\Rightarrow(10)^(-2)=(1)/(10^2) \\ (4^2)/(10^2) \end{gathered}`

Now, we also know that the quotient to a power rule is given by:

`((x)/(y))^m=(x^m)/(y^m)`

Therefore, we can say that:

`(4^2)/(10^2)=((4)/(10))^2`

Now, we can divide both the numerator and the denominator by 2 as follows (the fraction remains the same):

`\begin{gathered} (((4)/(2))/((10)/(2)))^2=((2)/(5))^2 \\ \end{gathered}`

And finally, applying the same rule as before - quotient to a power rule - we have:

`((2)/(5))^2=(2^2)/(5^2)=(4)/(25)=0.16`

In summary, therefore, the expression:

`4^2(10)^(-2)`

Can be simplified as (in square millimeters):

`(4)/(25)=0.16`