Calculus Examples

$- \frac{3 {(3)}^{2} (- 7)}{2 {(3)}^{3} - (- 7)}$

Step 1

Multiply $3$ by ${(3)}^{2}$ by adding the exponents.

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Step 1.1

Multiply $3$ by ${(3)}^{2}$ .

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Step 1.1.1

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

$- \frac{3^{1} {(3)}^{2} \cdot - 7}{2 {(3)}^{3} - (- 7)}$

Step 1.1.2

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

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

Step 1.2

Add $1$ and $2$ .

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

Step 2

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

$- \frac{27 \cdot - 7}{2 \cdot 3^{3} - (- 7)}$

Step 3

Simplify the denominator.

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Step 3.1

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

$- \frac{27 \cdot - 7}{2 \cdot 27 - (- 7)}$

Step 3.2

Multiply $2$ by $27$ .

$- \frac{27 \cdot - 7}{54 - (- 7)}$

Step 3.3

Multiply $- 1$ by $- 7$ .

$- \frac{27 \cdot - 7}{54 + 7}$

Step 3.4

Add $54$ and $7$ .

$- \frac{27 \cdot - 7}{61}$

Step 4

Simplify the expression.

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Step 4.1

Multiply $27$ by $- 7$ .

$- \frac{- 189}{61}$

Step 4.2

Move the negative in front of the fraction.

$- - \frac{189}{61}$

Step 5

Multiply $- - \frac{189}{61}$ .

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Step 5.1

Multiply $- 1$ by $- 1$ .

$1 (\frac{189}{61})$

Step 5.2

Multiply $\frac{189}{61}$ by $1$ .

$\frac{189}{61}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{189}{61}$

Decimal Form:

$3.09836065 \dots$

Mixed Number Form:

$3 \frac{6}{61}$