Algebra Examples

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

Step 1

Find the common denominator.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

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

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

Step 1.5

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

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

Step 1.6

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

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

Step 1.7

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

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

Step 1.8

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

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

Step 1.9

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

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

Step 2

Combine the numerators over the common denominator.

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

Step 3

Simplify each term.

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Step 3.1

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

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

Step 3.2

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

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

Step 3.3

Multiply $32$ by $9$ .

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

Step 3.4

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

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

Step 3.5

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

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

Step 3.6

Multiply $- 1$ by $6$ .

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

Step 3.7

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

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

Step 3.8

Multiply $- 6$ by $9$ .

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

Step 3.9

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

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

Step 3.10

Multiply $8$ by $9$ .

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

Step 4

Simplify the expression.

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Step 4.1

Subtract $54$ from $288$ .

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

Step 4.2

Subtract $45$ from $234$ .

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

Step 4.3

Add $189$ and $72$ .

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

Step 4.4

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

$\frac{261}{9}$

Step 4.5

Divide $261$ by $9$ .

$29$