Mat1182642_en (-7)² − (-7²) − (-7)² + 9 ÷ (9 ÷ 9 ÷ 9) = ?

 

ENGLISH VERSION
STEP-BY-STEP SOLUTION WITH PEMDAS

Problem: (-7)² − (-7²) − (-7)² + 9 ÷ (9 ÷ 9 ÷ 9) = ?

PEMDAS means:

P = Parentheses
E = Exponents
M = Multiplication
D = Division
A = Addition
S = Subtraction

IMPORTANT:

Multiplication and Division have the same priority, so they are calculated from LEFT TO RIGHT.

Addition and Subtraction also have the same priority, so they are calculated from LEFT TO RIGHT.

There is also an important difference between:

(-7)²

and

(-7²)

Step 1 — Calculate the Exponents

First:  (-7)² = 49

because:  (-7) × (-7) = 49

Now look at:  (-7²)

The exponent applies to 7 first:  7² = 49

Then the negative sign remains:  -7² = -49

Therefore:   (-7²) = -49

The third term is:   (-7)² = 49

So the expression becomes: 49 − (-49) − 49 + 9 ÷ (9 ÷ 9 ÷ 9)

Step 2 — Solve the Parentheses

Now solve: 9 ÷ 9 ÷ 9

Division has the same priority throughout, so calculate from LEFT TO RIGHT.

First: 9 ÷ 9 = 1

Then: 1 ÷ 9 = 1/9

Therefore:  (9 ÷ 9 ÷ 9) = 1/9

The expression becomes:  49 − (-49) − 49 + 9 ÷ 1/9

Step 3 — Division

Now calculate:  9 ÷ 1/9

Dividing by a fraction means multiplying by its reciprocal:

9 ÷ 1/9

= 9 × 9

= 81

So:  49 − (-49) − 49 + 81

Step 4 — Addition and Subtraction

Addition and subtraction have the same priority, so calculate from LEFT TO RIGHT.

First:  49 − (-49)

= 49 + 49

= 98

Then:  98 − 49 = 49

Then:  49 + 81 = 130

FINAL ANSWER:  130

 

ENGLISH VERSION
SUMMARY WITHOUT EXPLANATION

(-7)² − (-7²) − (-7)² + 9 ÷ (9 ÷ 9 ÷ 9) = ?

= 49 − (-49) − 49 + 9 ÷ (1/9)

= 49 + 49 − 49 + 81

= 98 − 49 + 81

= 49 + 81

= 130

ANSWER: 130

Problem Author: Aris Nurdiana (Public Platform: Facebook)

Step-by-Step Solution: Akur Atan (Accuracy)

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