Evaluate (2^5- square root of 36)-45÷(3^2)+8

$(2^{5} - \sqrt{36}) - 45 \div 3^{2} + 8$

Find the common denominator.

Write $2^{5}$ as a fraction with denominator $1$ .

$\frac{2^{5}}{1} - \sqrt{36} - 45 \div 3^{2} + 8$

Multiply $\frac{2^{5}}{1}$ by $\frac{3^{2}}{3^{2}}$ .

$\frac{2^{5}}{1} \cdot \frac{3^{2}}{3^{2}} - \sqrt{36} - 45 \div 3^{2} + 8$

Multiply $\frac{2^{5}}{1}$ by $\frac{3^{2}}{3^{2}}$ .

$\frac{2^{5} \cdot 3^{2}}{3^{2}} - \sqrt{36} - 45 \div 3^{2} + 8$

Write $- \sqrt{36}$ as a fraction with denominator $1$ .

$\frac{2^{5} \cdot 3^{2}}{3^{2}} + \frac{- \sqrt{36}}{1} - 45 \div 3^{2} + 8$

Multiply $\frac{- \sqrt{36}}{1}$ by $\frac{3^{2}}{3^{2}}$ .

$\frac{2^{5} \cdot 3^{2}}{3^{2}} + \frac{- \sqrt{36}}{1} \cdot \frac{3^{2}}{3^{2}} - 45 \div 3^{2} + 8$

Multiply $\frac{- \sqrt{36}}{1}$ by $\frac{3^{2}}{3^{2}}$ .

$\frac{2^{5} \cdot 3^{2}}{3^{2}} + \frac{- \sqrt{36} \cdot 3^{2}}{3^{2}} - 45 \div 3^{2} + 8$

Write $8$ as a fraction with denominator $1$ .

$\frac{2^{5} \cdot 3^{2}}{3^{2}} + \frac{- \sqrt{36} \cdot 3^{2}}{3^{2}} - 45 \div 3^{2} + \frac{8}{1}$

Multiply $\frac{8}{1}$ by $\frac{3^{2}}{3^{2}}$ .

$\frac{2^{5} \cdot 3^{2}}{3^{2}} + \frac{- \sqrt{36} \cdot 3^{2}}{3^{2}} - 45 \div 3^{2} + \frac{8}{1} \cdot \frac{3^{2}}{3^{2}}$

Multiply $\frac{8}{1}$ by $\frac{3^{2}}{3^{2}}$ .

$\frac{2^{5} \cdot 3^{2}}{3^{2}} + \frac{- \sqrt{36} \cdot 3^{2}}{3^{2}} - 45 \div 3^{2} + \frac{8 \cdot 3^{2}}{3^{2}}$

Combine the numerators over the common denominator.

$\frac{2^{5} \cdot 3^{2} - \sqrt{36} \cdot 3^{2} - 45 + 8 \cdot 3^{2}}{3^{2}}$

Simplify each term.

Raise $2$ to the power of $5$ .

$\frac{32 \cdot 3^{2} - \sqrt{36} \cdot 3^{2} - 45 + 8 \cdot 3^{2}}{3^{2}}$

Raise $3$ to the power of $2$ .

$\frac{32 \cdot 9 - \sqrt{36} \cdot 3^{2} - 45 + 8 \cdot 3^{2}}{3^{2}}$

Multiply $32$ by $9$ .

$\frac{288 - \sqrt{36} \cdot 3^{2} - 45 + 8 \cdot 3^{2}}{3^{2}}$

Rewrite $36$ as $6^{2}$ .

$\frac{288 - \sqrt{6^{2}} \cdot 3^{2} - 45 + 8 \cdot 3^{2}}{3^{2}}$

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

$\frac{288 - 1 \cdot 6 \cdot 3^{2} - 45 + 8 \cdot 3^{2}}{3^{2}}$

Multiply $- 1$ by $6$ .

$\frac{288 - 6 \cdot 3^{2} - 45 + 8 \cdot 3^{2}}{3^{2}}$

Raise $3$ to the power of $2$ .

$\frac{288 - 6 \cdot 9 - 45 + 8 \cdot 3^{2}}{3^{2}}$

Multiply $- 6$ by $9$ .

$\frac{288 - 54 - 45 + 8 \cdot 3^{2}}{3^{2}}$

Raise $3$ to the power of $2$ .

$\frac{288 - 54 - 45 + 8 \cdot 9}{3^{2}}$

Multiply $8$ by $9$ .

$\frac{288 - 54 - 45 + 72}{3^{2}}$

Simplify the expression.

Subtract $54$ from $288$ .

$\frac{234 - 45 + 72}{3^{2}}$

Subtract $45$ from $234$ .

$\frac{189 + 72}{3^{2}}$

Add $189$ and $72$ .

$\frac{261}{3^{2}}$

Raise $3$ to the power of $2$ .

$\frac{261}{9}$

Divide $261$ by $9$ .

$29$

Evaluate (2^5- square root of 36)-45÷(3^2)+8

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