What is (6-8)^2(5-7)^3 ?

The solution to (6-8)^2(5-7)^3 is -32

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(6-8)^2(5-7)^3

(6 - 8)^{2} (5 - 7)^{3}

- 32

Solution steps

(6 - 8)^{2} (5 - 7)^{3}

Follow the PEMDAS order of operations

Calculate within parentheses

(6 - 8) : - 2

6 - 8

6 - 8 = - 2

= - 2

= (- 2)^{2} (5 - 7)^{3}

Calculate within parentheses

(5 - 7) : - 2

5 - 7

5 - 7 = - 2

= - 2

= (- 2)^{2} (- 2)^{3}

Calculate exponents

(- 2)^{2} : 4

(- 2)^{2}

Apply exponent rule:

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

n

is even

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

= 4

= 4 (- 2)^{3}

Calculate exponents

(- 2)^{3} : - 8

(- 2)^{3}

Apply exponent rule:

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

n

is odd

(- 2)^{3} = - 2^{3} = - 8

= - 8

= 4 (- 8)

Multiply and divide (left to right)

4 (- 8) : - 32

4 (- 8)

Apply rule

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

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

= - 32

= - 32

7 - 5 \times 2 - 4^{1} - (- 4) + (3 + 5 \div 2)

- 13 + 46 + (- 17) + 8 + (+ 5)

1 + (1 - (- 1 - (- 1) - 1 + 1 + (- 1)))

7 \div 7 - 4 \times 5 - (- 10)

- 2 + 10 (- 4 + 3) (2) (- 4) (- 7) (- 3 \times 1)