What is [3-(4-2^3)^2]^2 ?

The solution to [3-(4-2^3)^2]^2 is 169

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[3-(4-2^3)^2]^2

[3 - (4 - 2^{3})^{2}]^{2}

169

Solution steps

[3 - (4 - 2^{3})^{2}]^{2}

Follow the PEMDAS order of operations

Calculate within parentheses

[3 - (4 - 2^{3})^{2}] : - 13

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

Calculate within parentheses

(4 - 2^{3}) : - 4

4 - 2^{3}

Calculate exponents

2^{3} : 8

2^{3}

2^{3} = 8

= 8

= 4 - 8

Add and subtract (left to right)

4 - 8 : - 4

4 - 8

4 - 8 = - 4

= - 4

= - 4

= 3 - (- 4)^{2}

Calculate exponents

(- 4)^{2} : 16

(- 4)^{2}

Apply exponent rule:

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

n

is even

(- 4)^{2} = 4^{2} = 16

= 16

= 3 - 16

Add and subtract (left to right)

3 - 16 : - 13

3 - 16

3 - 16 = - 13

= - 13

= - 13

= (- 13)^{2}

Calculate exponents

(- 13)^{2} : 169

(- 13)^{2}

Apply exponent rule:

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

n

is even

(- 13)^{2} = 1 3^{2} = 169

= 169

= 169

43 - 15 + 44 \times 30

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

10 - 6 \times (3 - 2) + (8 + 4)

\frac{1}{9} - 2 + \frac{4}{3}

4^{12} + 4^{10}