High School

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Simplify the expression using the order of operations.

[tex]
\[
\begin{aligned}
100 - 7^2 + 17 - 25 &= 100 - \square + 17 - 25 \\
&= \quad + 17 - 25 \\
&= \quad - 25 \\
&=
\end{aligned}
\]
[/tex]

Answer :

Sure! Let's simplify the expression [tex]\(100 - 7^2 + 17 - 25\)[/tex] step-by-step using the order of operations, which is sometimes remembered by the acronym PEMDAS/BODMAS (Parentheses/Brackets, Exponents/Orders, Multiplication and Division (left to right), Addition and Subtraction (left to right)).

1. Exponents: First, we calculate the exponent [tex]\(7^2\)[/tex]:
[tex]\[
7^2 = 49
\][/tex]
So, the expression becomes:
[tex]\[
100 - 49 + 17 - 25
\][/tex]

2. Subtraction and Addition from Left to Right:

- Subtract 49 from 100:
[tex]\[
100 - 49 = 51
\][/tex]
The expression now is:
[tex]\[
51 + 17 - 25
\][/tex]

- Add 17 to 51:
[tex]\[
51 + 17 = 68
\][/tex]
The expression now is:
[tex]\[
68 - 25
\][/tex]

- Finally, subtract 25 from 68:
[tex]\[
68 - 25 = 43
\][/tex]

So, the simplified expression is [tex]\(43\)[/tex].

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