Q5. - Algebra 1

Question

Evaluate each expression.

$\frac{{\left(2\cdot 4\right)}^2}{7+3^2}$

Step-by-Step Solution

Answer

The value of the given expression is 4.

Step 1. Order of operations.

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.

Step 2. Solving parentheses and exponent.

$\begin{array}{c}\frac{{\left(2\cdot 4\right)}^2}{7+3^2}=\frac{8^2}{7+3^2}\left[\text{Solving parentheses}\right]\\ =\frac{64}{7+9} \left[\text{Solving exponents}\right]\end{array}$

Step 3. Simplifying the expression.

$\begin{array}{c}\frac{64}{7+9}=\frac{64}{16}\left[\text{Performing Addition}\right]\\ =4 \left[\text{Performing division}\right]\end{array}$