Evaluate (8-3)^2-25÷5+(5-3)

${(8 - 3)}^{2} - 25 \div 5 + (5 - 3)$

Step 1

Remove parentheses.

${(8 - 3)}^{2} - 25 \div 5 + 5 - 3$

Step 2

Find the common denominator.

Write ${(8 - 3)}^{2}$ as a fraction with denominator $1$ .

$\frac{{(8 - 3)}^{2}}{1} - 25 \div 5 + 5 - 3$

Multiply $\frac{{(8 - 3)}^{2}}{1}$ by $\frac{5}{5}$ .

$\frac{{(8 - 3)}^{2}}{1} \cdot \frac{5}{5} - 25 \div 5 + 5 - 3$

Multiply $\frac{{(8 - 3)}^{2}}{1}$ by $\frac{5}{5}$ .

$\frac{{(8 - 3)}^{2} \cdot 5}{5} - 25 \div 5 + 5 - 3$

Write $5$ as a fraction with denominator $1$ .

$\frac{{(8 - 3)}^{2} \cdot 5}{5} - 25 \div 5 + \frac{5}{1} - 3$

Multiply $\frac{5}{1}$ by $\frac{5}{5}$ .

$\frac{{(8 - 3)}^{2} \cdot 5}{5} - 25 \div 5 + \frac{5}{1} \cdot \frac{5}{5} - 3$

Multiply $\frac{5}{1}$ by $\frac{5}{5}$ .

$\frac{{(8 - 3)}^{2} \cdot 5}{5} - 25 \div 5 + \frac{5 \cdot 5}{5} - 3$

Write $- 3$ as a fraction with denominator $1$ .

$\frac{{(8 - 3)}^{2} \cdot 5}{5} - 25 \div 5 + \frac{5 \cdot 5}{5} + \frac{- 3}{1}$

Multiply $\frac{- 3}{1}$ by $\frac{5}{5}$ .

$\frac{{(8 - 3)}^{2} \cdot 5}{5} - 25 \div 5 + \frac{5 \cdot 5}{5} + \frac{- 3}{1} \cdot \frac{5}{5}$

Multiply $\frac{- 3}{1}$ by $\frac{5}{5}$ .

$\frac{{(8 - 3)}^{2} \cdot 5}{5} - 25 \div 5 + \frac{5 \cdot 5}{5} + \frac{- 3 \cdot 5}{5}$

Step 3

Combine the numerators over the common denominator.

$\frac{{(8 - 3)}^{2} \cdot 5 - 25 + 5 \cdot 5 - 3 \cdot 5}{5}$

Step 4

Simplify each term.

Subtract $3$ from $8$ .

$\frac{5^{2} \cdot 5 - 25 + 5 \cdot 5 - 3 \cdot 5}{5}$

Multiply $5^{2}$ by $5$ by adding the exponents.

Multiply $5^{2}$ by $5$ .

Raise $5$ to the power of $1$ .

$\frac{5^{2} \cdot 5^{1} - 25 + 5 \cdot 5 - 3 \cdot 5}{5}$

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

$\frac{5^{2 + 1} - 25 + 5 \cdot 5 - 3 \cdot 5}{5}$

Add $2$ and $1$ .

$\frac{5^{3} - 25 + 5 \cdot 5 - 3 \cdot 5}{5}$

Raise $5$ to the power of $3$ .

$\frac{125 - 25 + 5 \cdot 5 - 3 \cdot 5}{5}$

Multiply $5$ by $5$ .

$\frac{125 - 25 + 25 - 3 \cdot 5}{5}$

Multiply $- 3$ by $5$ .

$\frac{125 - 25 + 25 - 15}{5}$

Step 5

Simplify the expression.

Subtract $25$ from $125$ .

$\frac{100 + 25 - 15}{5}$

Add $100$ and $25$ .

$\frac{125 - 15}{5}$

Subtract $15$ from $125$ .

$\frac{110}{5}$

Divide $110$ by $5$ .

$22$

Evaluate (8-3)^2-25÷5+(5-3)

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