What is 5\times 2^3-(-2)^5-(-2)^2+(-1)^7 ?

The solution to 5\times 2^3-(-2)^5-(-2)^2+(-1)^7 is 67

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5\times 2^3-(-2)^5-(-2)^2+(-1)^7

5 \cdot 2^{3} - (- 2)^{5} - (- 2)^{2} + (- 1)^{7}

67

Solution steps

5 \cdot 2^{3} - (- 2)^{5} - (- 2)^{2} + (- 1)^{7}

Follow the PEMDAS order of operations

Calculate exponents

2^{3} : 8

2^{3}

2^{3} = 8

= 8

= 5 \cdot 8 - (- 2)^{5} - (- 2)^{2} + (- 1)^{7}

Calculate exponents

(- 2)^{5} : - 32

(- 2)^{5}

Apply exponent rule:

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

n

is odd

(- 2)^{5} = - 2^{5} = - 32

= - 32

= 5 \cdot 8 - (- 32) - (- 2)^{2} + (- 1)^{7}

Calculate exponents

(- 2)^{2} : 4

(- 2)^{2}

Apply exponent rule:

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

n

is even

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

= 4

= 5 \cdot 8 - (- 32) - 4 + (- 1)^{7}

Calculate exponents

(- 1)^{7} : - 1

(- 1)^{7}

Apply exponent rule:

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

n

is odd

(- 1)^{7} = - 1^{7} = - 1

= - 1

= 5 \cdot 8 - (- 32) - 4 - 1

Multiply and divide (left to right)

5 \cdot 8 : 40

5 \cdot 8

5 \cdot 8 = 40

= 40

= 40 - (- 32) - 4 - 1

Add and subtract (left to right)

40 - (- 32) - 4 - 1 : 67

40 - (- 32) - 4 - 1

Apply rule

- (- a) = + a

- (- 32) = + 32

= 40 + 32 - 4 - 1

40 + 32 = 72

= 72 - 4 - 1

72 - 4 = 68

= 68 - 1

68 - 1 = 67

= 67

= 67

81 \div 9 - (3 \times 4 \times 5) + 64 - 32 \div 4

4 \times (- 2) - 5

(- 18) + (- 25) + 13

6 + (3 - 5 + 4) \times 2 - 3 \times (6 - 9 + 8)

(19 - 3^{4} + 2)^{2}

What is 5\times 2^3-(-2)^5-(-2)^2+(-1)^7 ?
The solution to 5\times 2^3-(-2)^5-(-2)^2+(-1)^7 is 67