What is -2(-2)^2+(-2)^6-4(-2)+1 ?

The solution to -2(-2)^2+(-2)^6-4(-2)+1 is 65

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-2(-2)^2+(-2)^6-4(-2)+1

- 2 (- 2)^{2} + (- 2)^{6} - 4 (- 2) + 1

65

Solution steps

- 2 (- 2)^{2} + (- 2)^{6} - 4 (- 2) + 1

Follow the PEMDAS order of operations

Calculate exponents

(- 2)^{2} : 4

(- 2)^{2}

Apply exponent rule:

(- a)^{n} = a^{n},

n

is even

(- 2)^{2} = 2^{2} = 4

= 4

= - 2 \cdot 4 + (- 2)^{6} - 4 (- 2) + 1

Calculate exponents

(- 2)^{6} : 64

(- 2)^{6}

Apply exponent rule:

(- a)^{n} = a^{n},

n

is even

(- 2)^{6} = 2^{6} = 64

= 64

= - 2 \cdot 4 + 64 - 4 (- 2) + 1

Multiply and divide (left to right)

- 2 \cdot 4 : - 8

- 2 \cdot 4

- 2 \cdot 4 = - 8

= - 8

= - 8 + 64 - 4 (- 2) + 1

Multiply and divide (left to right)

4 (- 2) : - 8

4 (- 2)

Apply rule

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

4 (- 2) = - 4 \cdot 2 = - 8

= - 8

= - 8 + 64 - (- 8) + 1

Add and subtract (left to right)

- 8 + 64 - (- 8) + 1 : 65

- 8 + 64 - (- 8) + 1

- 8 + 64 = 56

= 56 - (- 8) + 1

Apply rule

- (- a) = + a

- (- 8) = + 8

= 56 + 8 + 1

56 + 8 = 64

= 64 + 1

64 + 1 = 65

= 65

= 65

26 \cdot 26

\frac{64}{2} \cdot 16

\frac{15}{60}

- 3 (- 2)^{2}

\frac{125}{25}