Question

Evaluate each expression.

$\frac{8+3^3}{12-7}$

Short answer

The value of the expression $\frac{\mathbf{8}\mathbf{+}{\mathbf{3}}^{\mathbf{3}}}{\mathbf{12}\mathbf{-}\mathbf{7}}$is 7.

Step-by-step solution

Step 1. Order of operations.

In order to evaluate an expression, the order of operations must be followed, which is:

1. Evaluate the expressions inside the bracket
2. Evaluate the powers
3. Multiply and/or divide
4. Add and/ or subtract

The evaluation takes place from left to right.

Step 2. Evaluate the power in the numerator.

As per the order of operations, first, evaluate the power in the numerator.

$\frac{8+3^3}{12-7}=\frac{8+27}{12-7}$

Step 3. Apply subtraction and addition operations.

Subtract 7 from 12 in the denominator and add 8 and 27 in the numerator simultaneously.

$\begin{array}{l}\frac{8+3^3}{12-7}=\frac{8+27}{12-7}\\ =\frac{35}{5}\\ =7\end{array}$

Therefore, the expression is equal to 7.