Calculus Examples

$\frac{4}{5} \cdot {(81)}^{\frac{5}{4}} - \frac{4}{5} \cdot {(1)}^{\frac{5}{4}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $81$ as $3^{4}$ .

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

Step 1.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 1.3

Cancel the common factor of $4$ .

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Step 1.3.1

Cancel the common factor.

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

Step 1.3.2

Rewrite the expression.

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

Step 1.4

Raise $3$ to the power of $5$ .

$\frac{4}{5} \cdot 243 - \frac{4}{5} \cdot {(1)}^{\frac{5}{4}}$

Step 1.5

Multiply $\frac{4}{5} \cdot 243$ .

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Step 1.5.1

Combine $\frac{4}{5}$ and $243$ .

$\frac{4 \cdot 243}{5} - \frac{4}{5} \cdot {(1)}^{\frac{5}{4}}$

Step 1.5.2

Multiply $4$ by $243$ .

$\frac{972}{5} - \frac{4}{5} \cdot {(1)}^{\frac{5}{4}}$

Step 1.6

One to any power is one.

$\frac{972}{5} - \frac{4}{5} \cdot 1$

Step 1.7

Multiply $- 1$ by $1$ .

$\frac{972}{5} - \frac{4}{5}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{972 - 4}{5}$

Step 2.2

Subtract $4$ from $972$ .

$\frac{968}{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{968}{5}$

Decimal Form:

$193.6$

Mixed Number Form:

$193 \frac{3}{5}$