Let's evaluate the expression step-by-step:
[tex]\[
9^{\frac{3}{2}} + e^0 + \ln 1
\][/tex]
1. Evaluate [tex]\( 9^{\frac{3}{2}} \)[/tex]:
To find [tex]\( 9^{\frac{3}{2}} \)[/tex], we can rewrite it as a combination of a power and a root:
[tex]\[
9^{\frac{3}{2}} = (9^{\frac{1}{2}})^3
\][/tex]
The term [tex]\( 9^{\frac{1}{2}} \)[/tex] represents the square root of 9. The square root of 9 is 3. Therefore:
[tex]\[
9^{\frac{1}{2}} = 3
\][/tex]
Now, raising 3 to the power of 3, we get:
[tex]\[
(3)^3 = 27
\][/tex]
Thus:
[tex]\[
9^{\frac{3}{2}} = 27
\][/tex]
2. Evaluate [tex]\( e^0 \)[/tex]:
By definition, any number (except zero) raised to the power of 0 is 1:
[tex]\[
e^0 = 1
\][/tex]
3. Evaluate [tex]\( \ln 1 \)[/tex]:
The natural logarithm of 1 is always 0:
[tex]\[
\ln 1 = 0
\][/tex]
Now, we combine all the evaluated parts:
[tex]\[
9^{\frac{3}{2}} + e^0 + \ln 1 = 27 + 1 + 0 = 28
\][/tex]
Therefore, the value of the expression [tex]\( 9^{\frac{3}{2}} + e^0 + \ln 1 \)[/tex] is:
[tex]\[
\boxed{28}
\][/tex]
