Basic Math Examples

${(\frac{- 10 + 5 - (- 4)}{\frac{3^{3}}{3 - 2}})}^{3}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

${((- 10 + 5 - (- 4)) \frac{3 - 2}{3^{3}})}^{3}$

Step 2

Subtract $2$ from $3$ .

${((- 10 + 5 - (- 4)) \frac{1}{3^{3}})}^{3}$

Step 3

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

${((- 10 + 5 - (- 4)) \frac{1}{27})}^{3}$

Step 4

Multiply $- 1$ by $- 4$ .

${((- 10 + 5 + 4) \frac{1}{27})}^{3}$

Step 5

Add $- 10$ and $5$ .

${((- 5 + 4) \frac{1}{27})}^{3}$

Step 6

Add $- 5$ and $4$ .

${(- 1 (\frac{1}{27}))}^{3}$

Step 7

Rewrite $- 1 (\frac{1}{27})$ as $- (\frac{1}{27})$ .

${(- (\frac{1}{27}))}^{3}$

Step 8

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 8.1

Apply the product rule to $- \frac{1}{27}$ .

${(- 1)}^{3} {(\frac{1}{27})}^{3}$

Step 8.2

Apply the product rule to $\frac{1}{27}$ .

${(- 1)}^{3} \frac{1^{3}}{27^{3}}$

Step 9

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

$- \frac{1^{3}}{27^{3}}$

Step 10

One to any power is one.

$- \frac{1}{27^{3}}$

Step 11

Raise $27$ to the power of $3$ .

$- \frac{1}{19683}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{19683}$

Decimal Form:

$- 5.08052634 \cdot 10^{- 5}$