First, substitute $\displaystyle 2$ for $\displaystyle x$, $\displaystyle 3$ for $\displaystyle y$, and $\displaystyle 4$ for $\displaystyle 7$: $\displaystyle (2)^{3}-(4)^{2}+(2)^{4}$

Now, using the order of operations (Parentheses, Exponents, Multiplication, Division, Addittion, Subtraction), begin to simplify the expression:

$\displaystyle 8-16+16$

Leaving you with,

$\displaystyle 8$

First, substitute $\displaystyle 2$ for $\displaystyle a$, $\displaystyle 10$ for $\displaystyle b$, and $\displaystyle 3$ for $\displaystyle x$: $\displaystyle (3)(2+10)-(3)^{2}$

Now, using the order of operations (Parentheses, Exponents, Multiplication, Division, Addittion, Subtraction), begin to simplify the expression:

$\displaystyle (3)(12)-(9)$

$\displaystyle 36-9$

Leaving you with,

$\displaystyle 27$

First, substitute $\displaystyle 12$ for $\displaystyle c$ and $\displaystyle 11$ for $\displaystyle d$: $\displaystyle 14-2(12)+(11)^{2}-(12)^{2}$

Now, using the order of operations (Parentheses, Exponents, Multiplication, Division, Addittion, Subtraction), begin to simplify the expression:

$\displaystyle 14-2(12)+(121)-(144)$

$\displaystyle 14-24+121-144$

Leaving you with,

$\displaystyle -33$

First, substitute $\displaystyle 8$ for $\displaystyle x$ and $\displaystyle 11$ for $\displaystyle y$: $\displaystyle 5(11)+(8)^{2}((8)-7)$

Now, using the order of operations (Parentheses, Exponents, Multiplication, Division, Addittion, Subtraction), begin to simplify the expression:

$\displaystyle 5(11)+(64)(1)$

$\displaystyle 55+64$

Leaving you with,

$\displaystyle 119$

First, you subsitute $\displaystyle 6$ for $\displaystyle a$ and $\displaystyle 5$ for $\displaystyle b$: $\displaystyle (5)^{4}+3(6)-9$

Now, using the order of operations (Parentheses, Exponents, Multiplication, Division, Addittion, Subtraction), begin to simplify the expression:

$\displaystyle 625+3(6)-9$

$\displaystyle 625+18-9$

Leaving you with,

$\displaystyle 634$ 

To begin solving, first we would plug $\displaystyle 2$ in to $\displaystyle g(x)$ for every $\displaystyle x$ there is, making it:

$\displaystyle g(2)=(2)-3$

Solving, we get:

$\displaystyle g(2)=-1$

We would then put that solution into $\displaystyle f(x)$ for every $\displaystyle x$ there is, making it:

$\displaystyle f(g(2))=2(-1)^{2}+1$

Following the order of operations, the first thing we do is square $\displaystyle -1$:

$\displaystyle -1 \times -1 = 1$

We can then solve the rest of the expression:

$\displaystyle f(g(2))=2(1)+1$

$\displaystyle f(g(2))=3$

Evaluate the binomial squared first by order of operations.

$\displaystyle (x-6)^2 = (x-6)(x-6)$

$\displaystyle = x(x)+(x)(-6)+(-6)(x)+(-6)(-6)$

$\displaystyle x^2-12x+36$

The expression becomes:

$\displaystyle -6(x^2-12x+36)-3x+2$

Distribute the negative six through each term of the trinomial.

$\displaystyle -6x^2+72x-216-3x+2$

Combine like-terms.

The answer is:  $\displaystyle -6x^2+69x-214$

Substitute the value of $\displaystyle a$ into the given expression.

$\displaystyle 6(3)((3)^2-(3)^3)$

Simplify the parentheses by order of operations. 

$\displaystyle 18(9-27) = 18(-18) = -324$

The answer is:  $\displaystyle -324$

Substitute the assigned values into the expression.

$\displaystyle \frac{1}{b}-\frac{b}{a} = \frac{1}{6}-\frac{6}{5}$

Convert the fractions to a common denominator.

$\displaystyle \frac{1}{6}-\frac{6}{5} = \frac{1(5)}{6(5)}-\frac{6(6)}{5(6)} = \frac{5}{30}- \frac{36}{30}$

Now that the denominators are common, the numerators can be subtracted.

The answer is:  $\displaystyle -\frac{31}{30}$

Substitute the values into the expression.

$\displaystyle a(2-b)-a = 4(2-6)-4$

Simplify the expression by distribution.

$\displaystyle 4(2-6)-4 = 4(-4)-4 = -16-4 = -20$

The answer is:  $\displaystyle -20$