Linear Algebra Examples

$17.2 x^{12.86}$

Step 1

Convert expressions with fractional exponents to radicals.

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Step 1.1

Change $12.86$ into a fraction.

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Step 1.1.1

Multiply by $\frac{100}{100}$ to remove the decimal.

$17.2 x^{\frac{100 \cdot 12.86}{100}}$

Step 1.1.2

Multiply $100$ by $12.86$ .

$17.2 x^{\frac{1286}{100}}$

Step 1.1.3

Cancel the common factor of $1286$ and $100$ .

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Step 1.1.3.1

Factor $2$ out of $1286$ .

$17.2 x^{\frac{2 (643)}{100}}$

Step 1.1.3.2

Cancel the common factors.

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Step 1.1.3.2.1

Factor $2$ out of $100$ .

$17.2 x^{\frac{2 \cdot 643}{2 \cdot 50}}$

Step 1.1.3.2.2

Cancel the common factor.

$17.2 x^{\frac{2 \cdot 643}{2 \cdot 50}}$

Step 1.1.3.2.3

Rewrite the expression.

$17.2 x^{\frac{643}{50}}$

Step 1.2

Apply the rule $x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$ to rewrite the exponentiation as a radical.

$17.2 \sqrt[50]{x^{643}}$

Step 2

Set the radicand in $\sqrt[50]{x^{643}}$ greater than or equal to $0$ to find where the expression is defined.

$x^{643} \geq 0$

Step 3

Solve for $x$ .

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Step 3.1

Take the specified root of both sides of the inequality to eliminate the exponent on the left side.

$\sqrt[643]{x^{643}} \geq \sqrt[643]{0}$

Step 3.2

Simplify the equation.

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Step 3.2.1

Simplify the left side.

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Step 3.2.1.1

Pull terms out from under the radical.

$x \geq \sqrt[643]{0}$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Simplify $\sqrt[643]{0}$ .

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Step 3.2.2.1.1

Rewrite $0$ as $0^{643}$ .

$x \geq \sqrt[643]{0^{643}}$

Step 3.2.2.1.2

Pull terms out from under the radical.

$x \geq 0$

Step 4

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$[0, \infty)$

Set-Builder Notation:

${x | x \geq 0}$

Step 5