Algebra Examples

${(8 - 5)}^{3} - | 5^{2} - 4^{3} | \div 3$

Step 1

Simplify each term.

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Step 1.1

Subtract $5$ from $8$ .

$3^{3} - | 5^{2} - 4^{3} | \div 3$

Step 1.2

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

$27 - | 5^{2} - 4^{3} | \div 3$

Step 1.3

Rewrite the division as a fraction.

$27 - \frac{| 5^{2} - 4^{3} |}{3}$

Step 1.4

Simplify the numerator.

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Step 1.4.1

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

$27 - \frac{| 25 - 4^{3} |}{3}$

Step 1.4.2

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

$27 - \frac{| 25 - 1 \cdot 64 |}{3}$

Step 1.4.3

Multiply $- 1$ by $64$ .

$27 - \frac{| 25 - 64 |}{3}$

Step 1.4.4

Subtract $64$ from $25$ .

$27 - \frac{| - 39 |}{3}$

Step 1.4.5

The absolute value is the distance between a number and zero. The distance between $- 39$ and $0$ is $39$ .

$27 - \frac{39}{3}$

Step 1.5

Divide $39$ by $3$ .

$27 - 1 \cdot 13$

Step 1.6

Multiply $- 1$ by $13$ .

$27 - 13$

Step 2

Subtract $13$ from $27$ .

$14$