Evaluate ( square root of 9)/2-(2^3+(-3/2+8(10-3)))

$\frac{\sqrt{9}}{2} - (2^{3} + (- \frac{3}{2} + 8 (10 - 3)))$

Remove parentheses.

$\frac{\sqrt{9}}{2} - (2^{3} - \frac{3}{2} + 8 (10 - 3))$

Simplify each term.

Simplify the numerator.

Rewrite $9$ as $3^{2}$ .

$\frac{\sqrt{3^{2}}}{2} - (2^{3} - \frac{3}{2} + 8 (10 - 3))$

Pull terms out from under the radical, assuming positive real numbers.

$\frac{3}{2} - (2^{3} - \frac{3}{2} + 8 (10 - 3))$

Find the common denominator.

Write $2^{3}$ as a fraction with denominator $1$ .

$\frac{3}{2} - (\frac{2^{3}}{1} - \frac{3}{2} + 8 (10 - 3))$

Multiply $\frac{2^{3}}{1}$ by $\frac{2}{2}$ .

$\frac{3}{2} - (\frac{2^{3}}{1} \cdot \frac{2}{2} - \frac{3}{2} + 8 (10 - 3))$

Multiply $\frac{2^{3}}{1}$ by $\frac{2}{2}$ .

$\frac{3}{2} - (\frac{2^{3} \cdot 2}{2} - \frac{3}{2} + 8 (10 - 3))$

Write $8 (10 - 3)$ as a fraction with denominator $1$ .

$\frac{3}{2} - (\frac{2^{3} \cdot 2}{2} - \frac{3}{2} + \frac{8 (10 - 3)}{1})$

Multiply $\frac{8 (10 - 3)}{1}$ by $\frac{2}{2}$ .

$\frac{3}{2} - (\frac{2^{3} \cdot 2}{2} - \frac{3}{2} + \frac{8 (10 - 3)}{1} \cdot \frac{2}{2})$

Multiply $\frac{8 (10 - 3)}{1}$ by $\frac{2}{2}$ .

$\frac{3}{2} - (\frac{2^{3} \cdot 2}{2} - \frac{3}{2} + \frac{8 (10 - 3) \cdot 2}{2})$

Combine the numerators over the common denominator.

$\frac{3}{2} - \frac{2^{3} \cdot 2 - 3 + 8 (10 - 3) \cdot 2}{2}$

Simplify each term.

Multiply $2^{3}$ by $2$ by adding the exponents.

Multiply $2^{3}$ by $2$ .

Raise $2$ to the power of $1$ .

$\frac{3}{2} - \frac{2^{3} \cdot 2^{1} - 3 + 8 (10 - 3) \cdot 2}{2}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{3}{2} - \frac{2^{3 + 1} - 3 + 8 (10 - 3) \cdot 2}{2}$

Add $3$ and $1$ .

$\frac{3}{2} - \frac{2^{4} - 3 + 8 (10 - 3) \cdot 2}{2}$

Raise $2$ to the power of $4$ .

$\frac{3}{2} - \frac{16 - 3 + 8 (10 - 3) \cdot 2}{2}$

Subtract $3$ from $10$ .

$\frac{3}{2} - \frac{16 - 3 + 8 \cdot 7 \cdot 2}{2}$

Multiply $8$ by $7$ .

$\frac{3}{2} - \frac{16 - 3 + 56 \cdot 2}{2}$

Multiply $56$ by $2$ .

$\frac{3}{2} - \frac{16 - 3 + 112}{2}$

Subtract $3$ from $16$ .

$\frac{3}{2} - \frac{13 + 112}{2}$

Add $13$ and $112$ .

$\frac{3}{2} - \frac{125}{2}$

Combine fractions.

Combine the numerators over the common denominator.

$\frac{3 - 125}{2}$

Simplify the expression.

Subtract $125$ from $3$ .

$\frac{- 122}{2}$

Divide $- 122$ by $2$ .

$- 61$

Evaluate ( square root of 9)/2-(2^3+(-3/2+8(10-3)))

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