The solution to 3/2 (-2)^3 is -12

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3/2 (-2)^3

Solution

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

- 12

Solution steps

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

Follow the PEMDAS order of operations

Calculate exponents

(- 2)^{3} : - 8

(- 2)^{3}

Apply exponent rule:

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

n

is odd

(- 2)^{3} = - 2^{3} = - 8

= - 8

= \frac{3}{2} (- 8)

Multiply and divide (left to right)

\frac{3}{2} (- 8) : - 12

\frac{3}{2} (- 8)

Apply rule

a \cdot (- b) = - a \cdot b

\frac{3}{2} (- 8) = - \frac{3}{2} \cdot 8

Convert element to fraction:

8 = \frac{8}{1}

= - \frac{3}{2} \cdot \frac{8}{1}

Apply the fraction rule:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

\frac{3}{2} \cdot \frac{8}{1} = \frac{3 \cdot 8}{2 \cdot 1}

= - \frac{3 \cdot 8}{2 \cdot 1}

Cancel

\frac{3 \cdot 8}{2 \cdot 1} : 12

\frac{3 \cdot 8}{2 \cdot 1}

Multiply the numbers:

2 \cdot 1 = 2

= \frac{3 \cdot 8}{2}

Divide the numbers:

\frac{8}{2} = 4

= 3 \cdot 4

Multiply the numbers:

3 \cdot 4 = 12

= 12

= - 12

= - 12

\frac{- 1 - 2 ( \frac{9}{14} )}{4}

- 5 (6) + 4 (8)

(2 - 3)^{2} - 4

- 9 + (- 8) + 15 - 17 - (- 32) + 0

6 \times 3 - (2 + 5 \times 2) + (5 \times 3 - 8) - 1