Evaluate the function $h(x)=x^4-4x^2+5$ at the given values of the independent variable and simplify.
a. $h(-2)$
b. $h(-1)$
c. $h(-x)$
d. $h(3a)$
a. $h(-2)=5$ (Simplify your answer.)
b. $h(-1)=◻$ (Simplify your answer.)
c. $h(-x)=◻$ (Simplify your answer.)
d. $h(3a)=◻$ (Simplify your answer. $)$

Step 1 ：First, we substitute the given values into the function $h(x)=x^4-4x^2+5$.

Step 2 ：(b) For $h(-1)$, we substitute $x=-1$ into the function: $h(-1)=(-1{)}^4-4(-1{)}^2+5$

Step 3 ：Calculate the first part: $(-1{)}^4=1$

Step 4 ：Calculate the second part: $-4(-1{)}^2=-4$

Step 5 ：So, $h(-1)=1-4+5=\boxed{{\displaystyle 2}}$

Step 6 ：(c) For $h(-x)$, we substitute $x=-x$ into the function: $h(-x)=(-x{)}^4-4(-x{)}^2+5$

Step 7 ：Calculate the first part: $(-x{)}^4=x^4$

Step 8 ：Calculate the second part: $-4(-x{)}^2=-4x^2$

Step 9 ：So, $h(-x)=x^4-4x^2+5=\boxed{{\displaystyle x^4-4x^2+5}}$

Step 10 ：(d) For $h(3a)$, we substitute $x=3a$ into the function: $h(3a)=(3a{)}^4-4(3a{)}^2+5$

Step 11 ：Calculate the first part: $(3a{)}^4=81a^4$

Step 12 ：Calculate the second part: $-4(3a{)}^2=-36a^2$

Step 13 ：So, $h(3a)=81a^4-36a^2+5=\boxed{{\displaystyle 81a^4-36a^2+5}}$