How do you simplify 3^4+2 ^3+8(4times2-5) using order of operations?

Feb 3, 2016

${3}^{4} + {2}^{3} + 8 \left(4 \cdot 2 - 5\right)$

${3}^{4} = 3 \cdot 3 \cdot 3 \cdot 3 = 81$

${2}^{3} = 2 \cdot 2 \cdot 2 = 8$

So,

$\rightarrow 81 + 8 + 8 \left(4 \cdot 2 - 5\right)$

$\rightarrow 81 + 8 + 8 \left(3\right)$

$\rightarrow 81 + 8 + 24$

$\rightarrow 81 + 32 = 113$

Aug 25, 2016

$113$

Explanation:

Always count the number of terms first.
Each term must simplify to a single answer and they are added or subtracted in the last line.

Within a term, brackets are done first.
Powers and roots are strong operations and take priority over others
Multiplication and division are stronger than addition and subtraction.

Different operations can be done in the same line as long as they are independent of each other.

This expression has 3 terms.

$\textcolor{m a \ge n t a}{{3}^{4}} + \textcolor{b l u e}{{2}^{3}} + 8 \left(\textcolor{red}{4 \times 2} \textcolor{\mathmr{and} a n \ge}{- 5}\right)$

=$\textcolor{m a \ge n t a}{81} + \textcolor{b l u e}{8} + 8 \left(\textcolor{red}{8} \textcolor{\mathmr{and} a n \ge}{- 5}\right)$

=$\textcolor{m a \ge n t a}{81} + \textcolor{b l u e}{8} + 8 \left(\textcolor{red}{3}\right)$

=$\textcolor{m a \ge n t a}{81} + \textcolor{b l u e}{8} + 24$

=$113$