Calculus Examples

$4 {(0)}^{\frac{1}{4}} - \frac{\sqrt[4]{9}}{9}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $0$ as $0^{4}$ .

$4 {(0^{4})}^{\frac{1}{4}} - \frac{\sqrt[4]{9}}{9}$

Step 1.2

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

$4 \cdot 0^{4 (\frac{1}{4})} - \frac{\sqrt[4]{9}}{9}$

Step 1.3

Cancel the common factor of $4$ .

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Step 1.3.1

Cancel the common factor.

$4 \cdot 0^{4 (\frac{1}{4})} - \frac{\sqrt[4]{9}}{9}$

Step 1.3.2

Rewrite the expression.

$4 \cdot 0^{1} - \frac{\sqrt[4]{9}}{9}$

Step 1.4

Evaluate the exponent.

$4 \cdot 0 - \frac{\sqrt[4]{9}}{9}$

Step 1.5

Multiply $4$ by $0$ .

$0 - \frac{\sqrt[4]{9}}{9}$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Rewrite $9$ as $3^{2}$ .

$0 - \frac{\sqrt[4]{3^{2}}}{9}$

Step 1.6.2

Rewrite $\sqrt[4]{3^{2}}$ as $\sqrt{\sqrt{3^{2}}}$ .

$0 - \frac{\sqrt{\sqrt{3^{2}}}}{9}$

Step 1.6.3

Pull terms out from under the radical, assuming positive real numbers.

$0 - \frac{\sqrt{3}}{9}$

Step 2

Subtract $\frac{\sqrt{3}}{9}$ from $0$ .

$- \frac{\sqrt{3}}{9}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- \frac{\sqrt{3}}{9}$

Decimal Form:

$- 0.19245008 \dots$