Question

Evaluate each expression if $a=4$, $b=6$and $c=8$.

$\frac{b\left(9-c\right)}{a^2}$

Short answer

The value of the expression $\frac{\mathbf{b}\left(9-c\right)}{{\mathbf{a}}^{\mathbf{2}}}$is $\frac{\mathbf{3}}{\mathbf{8}}$.

Step-by-step solution

Step 1. Evaluation of algebraic expression.

To evaluate an expression with different operations, an order needs to be followed. The order is first we open the parenthesis then solve exponents then multiply and/or divide then finally add and/or subtract.

Step 2. Replace the variables.

Substitute 4 for a, 6 for b, and 8 for c into the equation $\frac{b\left(9-c\right)}{a^2}$.

$\frac{b\left(9-c\right)}{a^2}=\frac{6\left(9-8\right)}{4^2}$

Step 3. Apply the order of operations.

As per the order of operations, first, evaluate the expressions inside the bracket in the numerator, then evaluate the power in the denominator and simplify.

$\begin{array}{l}\frac{b\left(9-c\right)}{a^2}=\frac{6\left(1\right)}{4^2}\\ =\frac{6\cdot 1}{16}\\ =\frac{6}{16}\\ =\frac{3}{8}\end{array}$

Therefore, the expression is equal to $\frac{3}{8}$.