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

The solution to 3/2 (4^3-2^2*3^2) is 42

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

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

42

Solution steps

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

Follow the PEMDAS order of operations

Calculate within parentheses

(4^{3} - 2^{2} \cdot 3^{2}) : 28

4^{3} - 2^{2} \cdot 3^{2}

Calculate exponents

4^{3} : 64

4^{3}

4^{3} = 64

= 64

= 64 - 2^{2} \cdot 3^{2}

Calculate exponents

2^{2} : 4

2^{2}

2^{2} = 4

= 4

= 64 - 4 \cdot 3^{2}

Calculate exponents

3^{2} : 9

3^{2}

3^{2} = 9

= 9

= 64 - 4 \cdot 9

Multiply and divide (left to right)

4 \cdot 9 : 36

4 \cdot 9

4 \cdot 9 = 36

= 36

= 64 - 36

Add and subtract (left to right)

64 - 36 : 28

64 - 36

64 - 36 = 28

= 28

= 28

= \frac{3}{2} \cdot 28

Multiply and divide (left to right)

\frac{3}{2} \cdot 28 : 42

\frac{3}{2} \cdot 28

Convert element to fraction:

28 = \frac{28}{1}

= \frac{3}{2} \cdot \frac{28}{1}

Apply the fraction rule:

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

= \frac{3 \cdot 28}{2 \cdot 1}

Cancel

\frac{3 \cdot 28}{2 \cdot 1} : 42

\frac{3 \cdot 28}{2 \cdot 1}

Multiply the numbers:

2 \cdot 1 = 2

= \frac{3 \cdot 28}{2}

Divide the numbers:

\frac{28}{2} = 14

= 3 \cdot 14

Multiply the numbers:

3 \cdot 14 = 42

= 42

= 42

= 42

6 \times 3 - 12 - 2 + 7 - 4 \times 3

\frac{- 1}{2} - 5 \times \frac{- 3}{4}

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

(- 12)^{2} - 4 \times 4 \times 9

\frac{1}{2} - 8 (\frac{1}{4} + 1)