Question

Evaluate each expression.

$3^5-\left(1+{10}^2\right)$

Short answer

The value of the expression${\mathbf{3}}^{\mathbf{5}}\mathbf{-}\left(1+{10}^2\right)$ is 142.

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 expression inside the bracket.

In order to evaluate the expression inside the bracket, first, evaluate the power ${10}^2$.

$\begin{array}{l}{3}^5-\left(1+{10}^2\right)=3^5-\left(1+100\right)\\ =3^5-101\end{array}$

Step 3. Evaluate the power.

As per the order of operations, now evaluate the power $3^5$.

$3^5-\left(1+{10}^2\right)=243-101$

Step 4. Subtract 101 from 243.

Finally, subtract 101 from 243.

$3^5-\left(1+{10}^2\right)=142$

Therefore, the expression is equal to 142.