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

The solution to ((-2)^5-(-3)^3)^2 is 25

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

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

25

Solution steps

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

Follow the PEMDAS order of operations

Calculate within parentheses

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

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

Calculate exponents

(- 2)^{5} : - 32

(- 2)^{5}

Apply exponent rule:

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

n

is odd

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

= - 32

= - 32 - (- 3)^{3}

Calculate exponents

(- 3)^{3} : - 27

(- 3)^{3}

Apply exponent rule:

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

n

is odd

(- 3)^{3} = - 3^{3} = - 27

= - 27

= - 32 - (- 27)

Add and subtract (left to right)

- 32 - (- 27) : - 5

- 32 - (- 27)

Apply rule

- (- a) = + a

- (- 27) = + 27

= - 32 + 27

- 32 + 27 = - 5

= - 5

= - 5

= (- 5)^{2}

Calculate exponents

(- 5)^{2} : 25

(- 5)^{2}

Apply exponent rule:

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

n

is even

(- 5)^{2} = 5^{2} = 25

= 25

= 25

(\frac{1}{3} + \frac{2}{30}) + \frac{1}{6}

4 \times 7 + (136 \div 8) - 6 + (27 - 9) \times 2

1^{2} - 2 (1) - 3

(- 3)^{2} + 5 (- 3) + 9

2 \times 2^{2} + 5 \times 3 + 9