What is 1/2-2^3(3^2)+3-2^2(4^2) ?

The solution to 1/2-2^3(3^2)+3-2^2(4^2) is -265/2

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Popular >

1/2-2^3(3^2)+3-2^2(4^2)

Solution

\frac{1}{2} - 2^{3} (3^{2}) + 3 - 2^{2} (4^{2})

Solution

- \frac{265}{2}

Solution steps

\frac{1}{2} - 2^{3} (3^{2}) + 3 - 2^{2} (4^{2})

Follow the PEMDAS order of operations

Calculate within parentheses

(3^{2}) : 9

3^{2}

3^{2} = 9

= 9

= \frac{1}{2} - 2^{3} \cdot 9 + 3 - 2^{2} (4^{2})

Calculate within parentheses

(4^{2}) : 16

4^{2}

4^{2} = 16

= 16

= \frac{1}{2} - 2^{3} \cdot 9 + 3 - 2^{2} \cdot 16

Calculate exponents

2^{3} : 8

2^{3}

2^{3} = 8

= 8

= \frac{1}{2} - 8 \cdot 9 + 3 - 2^{2} \cdot 16

Calculate exponents

2^{2} : 4

2^{2}

2^{2} = 4

= 4

= \frac{1}{2} - 8 \cdot 9 + 3 - 4 \cdot 16

Multiply and divide (left to right)

8 \cdot 9 : 72

8 \cdot 9

8 \cdot 9 = 72

= 72

= \frac{1}{2} - 72 + 3 - 4 \cdot 16

Multiply and divide (left to right)

4 \cdot 16 : 64

4 \cdot 16

4 \cdot 16 = 64

= 64

= \frac{1}{2} - 72 + 3 - 64

Add and subtract (left to right)

\frac{1}{2} - 72 + 3 - 64 : - \frac{265}{2}

\frac{1}{2} - 72 + 3 - 64

\frac{1}{2} - 72 = - \frac{143}{2}

\frac{1}{2} - 72

Convert element to fraction:

72 = \frac{72 \cdot 2}{2}

= - \frac{72 \cdot 2}{2} + \frac{1}{2}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{- 72 \cdot 2 + 1}{2}

- 72 \cdot 2 + 1 = - 143

- 72 \cdot 2 + 1

Multiply the numbers:

72 \cdot 2 = 144

= - 144 + 1

Add/Subtract the numbers:

- 144 + 1 = - 143

= - 143

= \frac{- 143}{2}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{143}{2}

= - \frac{143}{2} + 3 - 64

- \frac{143}{2} + 3 = - \frac{137}{2}

- \frac{143}{2} + 3

Convert element to fraction:

3 = \frac{3 \cdot 2}{2}

= \frac{3 \cdot 2}{2} - \frac{143}{2}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{3 \cdot 2 - 143}{2}

3 \cdot 2 - 143 = - 137

3 \cdot 2 - 143

Multiply the numbers:

3 \cdot 2 = 6

= 6 - 143

Subtract the numbers:

6 - 143 = - 137

= - 137

= \frac{- 137}{2}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{137}{2}

= - \frac{137}{2} - 64

- \frac{137}{2} - 64 = - \frac{265}{2}

- \frac{137}{2} - 64

Convert element to fraction:

64 = \frac{64 \cdot 2}{2}

= - \frac{64 \cdot 2}{2} - \frac{137}{2}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{- 64 \cdot 2 - 137}{2}

- 64 \cdot 2 - 137 = - 265

- 64 \cdot 2 - 137

Multiply the numbers:

64 \cdot 2 = 128

= - 128 - 137

Subtract the numbers:

- 128 - 137 = - 265

= - 265

= \frac{- 265}{2}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{265}{2}

= - \frac{265}{2}

= - \frac{265}{2}

Popular Examples

-6-(-3)*7

- 6 - (- 3) \cdot 7

14*38-38*24

14 \cdot 38 - 38 \cdot 24

(4-(-5))^2

(4 - (- 5))^{2}

3\times 2^2-3

3 \times 2^{2} - 3

33492+44000-77490

33492 + 44000 - 77490

Frequently Asked Questions (FAQ)

What is 1/2-2^3(3^2)+3-2^2(4^2) ?
The solution to 1/2-2^3(3^2)+3-2^2(4^2) is -265/2