What is (3/2-10/4)^3 ?

The solution to (3/2-10/4)^3 is -1

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(3/2-10/4)^3

(\frac{3}{2} - \frac{10}{4})^{3}

- 1

Solution steps

(\frac{3}{2} - \frac{10}{4})^{3}

\frac{10}{4} = \frac{5}{2}

Cancel the common factor:

2

\frac{5}{2}

= (\frac{3}{2} - \frac{5}{2})^{3}

Follow the PEMDAS order of operations

Calculate within parentheses

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

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

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

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

Apply rule

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

= \frac{3 - 5}{2}

Subtract the numbers:

3 - 5 = - 2

= \frac{- 2}{2}

Apply the fraction rule:

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

= - \frac{2}{2}

Apply rule

\frac{a}{a} = 1

= - 1

= - 1

= (- 1)^{3}

Calculate exponents

(- 1)^{3} : - 1

(- 1)^{3}

Apply exponent rule:

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

n

is odd

(- 1)^{3} = - 1^{3} = - 1

= - 1

= - 1

8 - 4 (3) (- 2)^{3}

8 - 4 (3) (- 2)^{2}

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

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

- 5 (6) + 4 (8)