What is 1+(-6)+(-6)^2+(-6)^3+(-6)^4 ?

The solution to 1+(-6)+(-6)^2+(-6)^3+(-6)^4 is 1111

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1+(-6)+(-6)^2+(-6)^3+(-6)^4

1 + (- 6) + (- 6)^{2} + (- 6)^{3} + (- 6)^{4}

1111

Solution steps

1 + (- 6) + (- 6)^{2} + (- 6)^{3} + (- 6)^{4}

Follow the PEMDAS order of operations

Calculate exponents

(- 6)^{2} : 36

(- 6)^{2}

Apply exponent rule:

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

n

is even

(- 6)^{2} = 6^{2} = 36

= 36

= 1 + (- 6) + 36 + (- 6)^{3} + (- 6)^{4}

Calculate exponents

(- 6)^{3} : - 216

(- 6)^{3}

Apply exponent rule:

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

n

is odd

(- 6)^{3} = - 6^{3} = - 216

= - 216

= 1 + (- 6) + 36 - 216 + (- 6)^{4}

Calculate exponents

(- 6)^{4} : 1296

(- 6)^{4}

Apply exponent rule:

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

n

is even

(- 6)^{4} = 6^{4} = 1296

= 1296

= 1 + (- 6) + 36 - 216 + (- 6)^{4}

Add and subtract (left to right)

1 + (- 6) + 36 - 216 + (- 6)^{4} : 1111

1 + (- 6) + 36 - 216 + (- 6)^{4}

Apply rule

+ (- a) = - a

+ (- 6) = - 6

= 1 - 6 + 36 - 216 + (- 6)^{4}

1 - 6 = - 5

= - 5 + 36 - 216 + (- 6)^{4}

- 5 + 36 = 31

= 31 - 216 + (- 6)^{4}

31 - 216 = - 185

= - 185 + (- 6)^{4}

- 185 + (- 6)^{4} = 1111

= 1111

= 1111

19 + 2 - 10 + 15 - 12 + 15 - 12 + 7

19 - 4 \div 2 \times 5 - 7

0 - 1 - 1

1 2^{2} - 4^{3} + 4^{2}

6 - 2 \times (1 - 3)

What is 1+(-6)+(-6)^2+(-6)^3+(-6)^4 ?
The solution to 1+(-6)+(-6)^2+(-6)^3+(-6)^4 is 1111