Evaluate 2(5-2)^3-15÷3+7

$2 {(5 - 2)}^{3} - 15 \div 3 + 7$

Find the common denominator.

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Write $2 {(5 - 2)}^{3}$ as a fraction with denominator $1$ .

$\frac{2 {(5 - 2)}^{3}}{1} - 15 \div 3 + 7$

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

$\frac{2 {(5 - 2)}^{3}}{1} \cdot \frac{3}{3} - 15 \div 3 + 7$

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

$\frac{2 {(5 - 2)}^{3} \cdot 3}{3} - 15 \div 3 + 7$

Write $7$ as a fraction with denominator $1$ .

$\frac{2 {(5 - 2)}^{3} \cdot 3}{3} - 15 \div 3 + \frac{7}{1}$

Multiply $\frac{7}{1}$ by $\frac{3}{3}$ .

$\frac{2 {(5 - 2)}^{3} \cdot 3}{3} - 15 \div 3 + \frac{7}{1} \cdot \frac{3}{3}$

Multiply $\frac{7}{1}$ and $\frac{3}{3}$ .

$\frac{2 {(5 - 2)}^{3} \cdot 3}{3} - 15 \div 3 + \frac{7 \cdot 3}{3}$

Combine fractions with similar denominators.

$\frac{2 {(5 - 2)}^{3} \cdot 3 - 15 + 7 \cdot 3}{3}$

Simplify the expression.

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Subtract $2$ from $5$ .

$\frac{2 \cdot 3^{3} \cdot 3 - 15 + 7 \cdot 3}{3}$

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

$\frac{2 \cdot 27 \cdot 3 - 15 + 7 \cdot 3}{3}$

Multiply $2$ by $27$ .

$\frac{54 \cdot 3 - 15 + 7 \cdot 3}{3}$

Multiply $54$ by $3$ .

$\frac{162 - 15 + 7 \cdot 3}{3}$

Multiply $7$ by $3$ .

$\frac{162 - 15 + 21}{3}$

Reduce the expression $\frac{162 - 15 + 21}{3}$ by cancelling the common factors.

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Factor $3$ out of $162$ .

$\frac{3 \cdot 54 - 15 + 21}{3}$

Factor $3$ out of $- 15$ .

$\frac{3 \cdot 54 + 3 \cdot - 5 + 21}{3}$

Factor $3$ out of $3 \cdot 54 + 3 \cdot - 5$ .

$\frac{3 \cdot (54 - 5) + 21}{3}$

Factor $3$ out of $21$ .

$\frac{3 \cdot (54 - 5) + 3 \cdot 7}{3}$

Factor $3$ out of $3 \cdot (54 - 5) + 3 (7)$ .

$\frac{3 \cdot (54 - 5 + 7)}{3}$

Factor $3$ out of $3$ .

$\frac{3 \cdot (54 - 5 + 7)}{3 (1)}$

Cancel the common factor.

$\frac{3 \cdot (54 - 5 + 7)}{3 \cdot 1}$

Rewrite the expression.

$\frac{54 - 5 + 7}{1}$

Simplify the expression.

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Divide $54 - 5 + 7$ by $1$ .

$54 - 5 + 7$

Subtract $5$ from $54$ .

$49 + 7$

Add $49$ and $7$ .

$56$