Evaluate 4(5-2)^3-45÷3+7

$4 {(5 - 2)}^{3} - 45 \div 3 + 7$

Step 1

Find the common denominator.

Write $4 {(5 - 2)}^{3}$ as a fraction with denominator $1$ .

$\frac{4 {(5 - 2)}^{3}}{1} - 45 \div 3 + 7$

Multiply $\frac{4 {(5 - 2)}^{3}}{1}$ by $\frac{3}{3}$ .

$\frac{4 {(5 - 2)}^{3}}{1} \cdot \frac{3}{3} - 45 \div 3 + 7$

Multiply $\frac{4 {(5 - 2)}^{3}}{1}$ by $\frac{3}{3}$ .

$\frac{4 {(5 - 2)}^{3} \cdot 3}{3} - 45 \div 3 + 7$

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

$\frac{4 {(5 - 2)}^{3} \cdot 3}{3} - 45 \div 3 + \frac{7}{1}$

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

$\frac{4 {(5 - 2)}^{3} \cdot 3}{3} - 45 \div 3 + \frac{7}{1} \cdot \frac{3}{3}$

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

$\frac{4 {(5 - 2)}^{3} \cdot 3}{3} - 45 \div 3 + \frac{7 \cdot 3}{3}$

Step 2

Combine the numerators over the common denominator.

$\frac{4 {(5 - 2)}^{3} \cdot 3 - 45 + 7 \cdot 3}{3}$

Step 3

Simplify each term.

Subtract $2$ from $5$ .

$\frac{4 \cdot 3^{3} \cdot 3 - 45 + 7 \cdot 3}{3}$

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

Move $3$ .

$\frac{4 \cdot (3 \cdot 3^{3}) - 45 + 7 \cdot 3}{3}$

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

Raise $3$ to the power of $1$ .

$\frac{4 \cdot (3^{1} \cdot 3^{3}) - 45 + 7 \cdot 3}{3}$

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

$\frac{4 \cdot 3^{1 + 3} - 45 + 7 \cdot 3}{3}$

Add $1$ and $3$ .

$\frac{4 \cdot 3^{4} - 45 + 7 \cdot 3}{3}$

Raise $3$ to the power of $4$ .

$\frac{4 \cdot 81 - 45 + 7 \cdot 3}{3}$

Multiply $4$ by $81$ .

$\frac{324 - 45 + 7 \cdot 3}{3}$

Multiply $7$ by $3$ .

$\frac{324 - 45 + 21}{3}$

Step 4

Simplify the expression.

Subtract $45$ from $324$ .

$\frac{279 + 21}{3}$

Add $279$ and $21$ .

$\frac{300}{3}$

Divide $300$ by $3$ .

$100$