Question

4. Evaluate $a^3+b\left(9-c\right)$ if $a=-2,b=\frac{1}{3},$ and $c=-12$

Short answer

Expression $a^3+b\left(9-c\right)$ results into $-1$

Step-by-step solution

- Order for simplification 

To evaluate any expression involving more than one operation, follow the below order of operations:

• First evaluate expressions inside grouping symbols like parentheses ( ) or brackets [ ].
• Evaluate the exponents.
• Perform Multiplication and division from left to right.
• Perform addition and subtraction from left to right.

- Substitution

Substitute $-2$for a, $\frac{1}{3}$for b, and $-12$for c in given expression.

$a^3+b\left(9-c\right)={\left(-2\right)}^3+\frac{1}{3}\left(9-\left(-12\right)\right)$

- Simplify expression inside grouping symbol

To evaluate the value of the given expression, first simplify parentheses as shown below

$\begin{array}{c}{\left(-2\right)}^3+\frac{1}{3}\left(9-\left(-12\right)\right)=-8+\frac{1}{3}\left(9+12\right)\\ =-8+\frac{1}{3}\left(21\right)\\ =-8+7\end{array}$

- Add -8 with 7

Now, to simplify further add the numbers to get,

$-8+7=-1$