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

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

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4(3/2-10/4)^3

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

- 4

Solution steps

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

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

Cancel the common factor:

2

\frac{5}{2}

= 4 (\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

= 4 (- 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

= 4 (- 1)

Multiply and divide (left to right)

4 (- 1) : - 4

4 (- 1)

Apply rule

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

4 (- 1) = - 4 \cdot 1 = - 4

= - 4

= - 4

9 - 3 + (4^{2} - 10) + 4

32 - (- 5) (6)

\frac{( - 5 ) ^{2} + 10 ( - 5 ) + 25}{2 ( - 5 ) + 1}

2 \cdot 7^{3}

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