Calculus Examples

$(\frac{3 {(3)}^{\frac{4}{3}}}{4} - 9) - (\frac{3 {(- 3)}^{\frac{4}{3}}}{4} + 9)$

Step 1

Simplify each term.

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Step 1.1

Multiply $3$ by ${(3)}^{\frac{4}{3}}$ by adding the exponents.

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Step 1.1.1

Multiply $3$ by ${(3)}^{\frac{4}{3}}$ .

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Step 1.1.1.1

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

$\frac{3^{1} {(3)}^{\frac{4}{3}}}{4} - 9 - (\frac{3 {(- 3)}^{\frac{4}{3}}}{4} + 9)$

Step 1.1.1.2

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

$\frac{3^{1 + \frac{4}{3}}}{4} - 9 - (\frac{3 {(- 3)}^{\frac{4}{3}}}{4} + 9)$

Step 1.1.2

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

$\frac{3^{\frac{3}{3} + \frac{4}{3}}}{4} - 9 - (\frac{3 {(- 3)}^{\frac{4}{3}}}{4} + 9)$

Step 1.1.3

Combine the numerators over the common denominator.

$\frac{3^{\frac{3 + 4}{3}}}{4} - 9 - (\frac{3 {(- 3)}^{\frac{4}{3}}}{4} + 9)$

Step 1.1.4

Add $3$ and $4$ .

$\frac{3^{\frac{7}{3}}}{4} - 9 - (\frac{3 {(- 3)}^{\frac{4}{3}}}{4} + 9)$

Step 1.2

To write $9$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{3^{\frac{7}{3}}}{4} - 9 - (\frac{3 {(- 3)}^{\frac{4}{3}}}{4} + 9 \cdot \frac{4}{4})$

Step 1.3

Combine $9$ and $\frac{4}{4}$ .

$\frac{3^{\frac{7}{3}}}{4} - 9 - (\frac{3 {(- 3)}^{\frac{4}{3}}}{4} + \frac{9 \cdot 4}{4})$

Step 1.4

Combine the numerators over the common denominator.

$\frac{3^{\frac{7}{3}}}{4} - 9 - \frac{3 {(- 3)}^{\frac{4}{3}} + 9 \cdot 4}{4}$

Step 1.5

Multiply $9$ by $4$ .

$\frac{3^{\frac{7}{3}}}{4} - 9 - \frac{3 {(- 3)}^{\frac{4}{3}} + 36}{4}$

Step 2

To write $- 9$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{3^{\frac{7}{3}}}{4} - 9 \cdot \frac{4}{4} - \frac{3 {(- 3)}^{\frac{4}{3}} + 36}{4}$

Step 3

Combine fractions.

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Step 3.1

Combine $- 9$ and $\frac{4}{4}$ .

$\frac{3^{\frac{7}{3}}}{4} + \frac{- 9 \cdot 4}{4} - \frac{3 {(- 3)}^{\frac{4}{3}} + 36}{4}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{3^{\frac{7}{3}} - 9 \cdot 4}{4} - \frac{3 {(- 3)}^{\frac{4}{3}} + 36}{4}$

Step 3.3

Combine the numerators over the common denominator.

$\frac{3^{\frac{7}{3}} - 9 \cdot 4 - (3 {(- 3)}^{\frac{4}{3}} + 36)}{4}$

Step 4

Simplify each term.

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Step 4.1

Multiply $- 9$ by $4$ .

$\frac{3^{\frac{7}{3}} - 36 - (3 {(- 3)}^{\frac{4}{3}} + 36)}{4}$

Step 4.2

Apply the distributive property.

$\frac{3^{\frac{7}{3}} - 36 - (3 {(- 3)}^{\frac{4}{3}}) - 1 \cdot 36}{4}$

Step 4.3

Multiply $- (3 {(- 3)}^{\frac{4}{3}})$ .

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Step 4.3.1

Multiply $3$ by $- 1$ .

$\frac{3^{\frac{7}{3}} - 36 - 3 {(- 3)}^{\frac{4}{3}} - 1 \cdot 36}{4}$

Step 4.3.2

Multiply $- 3$ by ${(- 3)}^{\frac{4}{3}}$ by adding the exponents.

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Step 4.3.2.1

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

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Step 4.3.2.1.1

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

$\frac{3^{\frac{7}{3}} - 36 + {(- 3)}^{1} {(- 3)}^{\frac{4}{3}} - 1 \cdot 36}{4}$

Step 4.3.2.1.2

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

$\frac{3^{\frac{7}{3}} - 36 + {(- 3)}^{1 + \frac{4}{3}} - 1 \cdot 36}{4}$

Step 4.3.2.2

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

$\frac{3^{\frac{7}{3}} - 36 + {(- 3)}^{\frac{3}{3} + \frac{4}{3}} - 1 \cdot 36}{4}$

Step 4.3.2.3

Combine the numerators over the common denominator.

$\frac{3^{\frac{7}{3}} - 36 + {(- 3)}^{\frac{3 + 4}{3}} - 1 \cdot 36}{4}$

Step 4.3.2.4

Add $3$ and $4$ .

$\frac{3^{\frac{7}{3}} - 36 + {(- 3)}^{\frac{7}{3}} - 1 \cdot 36}{4}$

Step 4.4

Multiply $- 1$ by $36$ .

$\frac{3^{\frac{7}{3}} - 36 + {(- 3)}^{\frac{7}{3}} - 36}{4}$

Step 5

Subtract $36$ from $- 36$ .

$\frac{3^{\frac{7}{3}} - 72 + {(- 3)}^{\frac{7}{3}}}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{3^{\frac{7}{3}} - 72 + {(- 3)}^{\frac{7}{3}}}{4}$

Decimal Form:

$- 18$