Question

Evaluate each expression.

$\frac{\left(1+6\right)9}{5^2-4}$

Short answer

The value of the expression $\frac{\left(1+6\right)\mathbf{9}}{{\mathbf{5}}^{\mathbf{2}}\mathbf{-}\mathbf{4}}$is 3.

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 bracket.

As per the order of operations, first, evaluate the expression inside the bracket in the numerator.

$\frac{\left(1+6\right)9}{5^2-4}=\frac{7\cdot 9}{5^2-4}$

Step 3. Evaluate the power.

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

$\frac{\left(1+6\right)9}{5^2-4}=\frac{7\cdot 9}{25-4}$

Step 4. Apply multiplication and subtraction operations.

First, multiply 7 by 9 in numerator followed by subtraction of 4 from 25 in the denominator and simplify.

$\begin{array}{l}\frac{\left(1+6\right)9}{5^2-4}=\frac{7\cdot 9}{25-4}\\ =\frac{63}{25-4}\\ =\frac{63}{21}\\ =3\end{array}$

Therefore, the expression is equal to 3.