To solve the given expression [tex]\( \frac{1}{2^2 + 4(5)} \)[/tex], let's break it down step by step:
1. Calculate the exponent part:
[tex]\[
2^2
\][/tex]
This means [tex]\(2\)[/tex] raised to the power of [tex]\(2\)[/tex]:
[tex]\[
2^2 = 4
\][/tex]
2. Calculate the multiplication part:
[tex]\[
4(5)
\][/tex]
This is simply [tex]\(4\)[/tex] multiplied by [tex]\(5\)[/tex]:
[tex]\[
4 \times 5 = 20
\][/tex]
3. Add the results from the exponent part and the multiplication part:
[tex]\[
2^2 + 4(5) = 4 + 20 = 24
\][/tex]
4. Define the fraction:
[tex]\[
\frac{1}{24}
\][/tex]
Simplifying this fraction, we get:
[tex]\[
\frac{1}{24} \approx 0.041666666666666664
\][/tex]
Therefore, the final result of the expression [tex]\( \frac{1}{2^2 + 4(5)} \)[/tex] is approximately [tex]\( 0.041666666666666664 \)[/tex].
