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

1^{2} + 2^{2}

3^{2} + 2

- 3 (0)^{2}

4 \cdot 4^{2}

4^{2} + 7^{2}