Mat1182641_en (-5)² − (-5)² − (-5²) + 5² : (5 : 5 : 5) = ?

 

ENGLISH VERSION
STEP-BY-STEP SOLUTION WITH PEMDAS

Problem: (-5)² − (-5)² − (-5²) + 5² ÷ (5 ÷ 5 ÷ 5) = ?

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 performed from left to right.

Addition and subtraction also have the same priority, so they are performed from left to right.

Step 1 — Evaluate the exponents

First:   (-5)² = 25

because:   (-5) × (-5) = 25

The second one is also:   (-5)² = 25

Now pay close attention to:   (-5²)

The exponent applies to 5 first:   5² = 25

Then the negative sign remains:   -5² = -25

Therefore:   (-5²) = -25

Also:   5² = 25

So the expression becomes:   25 − 25 − (-25) + 25 ÷ (5 ÷ 5 ÷ 5)

Step 2 — Solve the parentheses

We have:   5 ÷ 5 ÷ 5

Division must be performed from left to right.

First: 5 ÷ 5 = 1

Then: 1 ÷ 5 = 1/5

Therefore: (5 ÷ 5 ÷ 5) = 1/5

Now the expression becomes:   25 − 25 − (-25) + 25 ÷ 1/5

Step 3 — Division

Now calculate:   25 ÷ 1/5

Dividing by a fraction means multiplying by its reciprocal:

25 ÷ 1/5

= 25 × 5

= 125

So:   25 − 25 − (-25) + 125

Step 4 — Addition and subtraction

Work from left to right:

25 − 25 = 0

Then:

0 − (-25)

= 0 + 25

= 25

Then:

25 + 125

= 150

FINAL ANSWER:   150

Therefore:

101 is NOT correct.

 

 

ENGLISH VERSION
SUMMARY WITHOUT EXPLANATION

(-5)² − (-5)² − (-5²) + 5² ÷ (5 ÷ 5 ÷ 5) = ?

= 25 − 25 − (-25) + 25 ÷ (1/5)

= 25 − 25 + 25 + 125

= 0 + 25 + 125

= 150

ANSWER: 150

Problem Author: Aris Nurdiana (Public Platform: Facebook)

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

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