What is 5(3-2(-2)+(2-3))^2 ?

The solution to 5(3-2(-2)+(2-3))^2 is 180

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5(3-2(-2)+(2-3))^2

5 (3 - 2 (- 2) + (2 - 3))^{2}

180

Solution steps

5 (3 - 2 (- 2) + (2 - 3))^{2}

Follow the PEMDAS order of operations

Calculate within parentheses

(3 - 2 (- 2) + (2 - 3)) : 6

3 - 2 (- 2) + (2 - 3)

Calculate within parentheses

(2 - 3) : - 1

2 - 3

2 - 3 = - 1

= - 1

= 3 - 2 (- 2) - 1

Multiply and divide (left to right)

2 (- 2) : - 4

2 (- 2)

Apply rule

a \cdot (- b) = - a \cdot b

2 (- 2) = - 2 \cdot 2 = - 4

= - 4

= 3 - (- 4) - 1

Add and subtract (left to right)

3 - (- 4) - 1 : 6

3 - (- 4) - 1

Apply rule

- (- a) = + a

- (- 4) = + 4

= 3 + 4 - 1

3 + 4 = 7

= 7 - 1

7 - 1 = 6

= 6

= 6

= 5 \cdot 6^{2}

Calculate exponents

6^{2} : 36

6^{2}

6^{2} = 36

= 36

= 5 \cdot 36

Multiply and divide (left to right)

5 \cdot 36 : 180

5 \cdot 36

5 \cdot 36 = 180

= 180

= 180

8 5^{2} - 3 6^{2}

8 + 8 - 6 - 2 - 10 + 8

8 + 4 - 3

(0)^{4} - (0)^{2} + 1

9 (- 3)^{2}