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

The solution to 1/2 (-1)^2-3 is -5/2

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1/2 (-1)^2-3

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

- \frac{5}{2}

Solution steps

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

Follow the PEMDAS order of operations

Calculate exponents

(- 1)^{2} : 1

(- 1)^{2}

Apply exponent rule:

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

n

is even

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

= 1

= \frac{1}{2} \cdot 1 - 3

Multiply and divide (left to right)

\frac{1}{2} \cdot 1 : \frac{1}{2}

\frac{1}{2} \cdot 1

\frac{1}{2} \cdot 1 = \frac{1}{2}

= \frac{1}{2}

= \frac{1}{2} - 3

Add and subtract (left to right)

\frac{1}{2} - 3 : - \frac{5}{2}

\frac{1}{2} - 3

\frac{1}{2} - 3 = - \frac{5}{2}

\frac{1}{2} - 3

Convert element to fraction:

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

= - \frac{3 \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{- 3 \cdot 2 + 1}{2}

- 3 \cdot 2 + 1 = - 5

- 3 \cdot 2 + 1

Multiply the numbers:

3 \cdot 2 = 6

= - 6 + 1

Add/Subtract the numbers:

- 6 + 1 = - 5

= - 5

= \frac{- 5}{2}

Apply the fraction rule:

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

= - \frac{5}{2}

= - \frac{5}{2}

= - \frac{5}{2}

3^{2} \cdot (3 - 1)^{2} + 2^{3} \cdot (15 - 13)

13 + 17 - 10 + 13

\frac{3 ^{2} - 2 ( 3 ) + 12}{4 ( 1 ) - 1}

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

7 - (3^{2} - 5) - 6 \times 3