Linear Algebra Examples

{(\sqrt[5750]{0.5})}^{4000}

${(\sqrt[5750]{0.5})}^{4000}$

Step 1

Rewrite

{\sqrt[5750]{0.5}}^{4000}

${\sqrt[5750]{0.5}}^{4000}$ as

\sqrt[5750]{{0.5}^{4000}}

$\sqrt[5750]{{0.5}^{4000}}$ .

\sqrt[5750]{{0.5}^{4000}}

$\sqrt[5750]{{0.5}^{4000}}$

Step 2

Rewrite

{0.5}^{4000}

${0.5}^{4000}$ as

{({0.5}^{80})}^{50}

${({0.5}^{80})}^{50}$ .

\sqrt[5750]{{({0.5}^{80})}^{50}}

$\sqrt[5750]{{({0.5}^{80})}^{50}}$

Step 3

Rewrite

\sqrt[5750]{{({0.5}^{80})}^{50}}

$\sqrt[5750]{{({0.5}^{80})}^{50}}$ as

\sqrt[115]{\sqrt[50]{{({0.5}^{80})}^{50}}}

$\sqrt[115]{\sqrt[50]{{({0.5}^{80})}^{50}}}$ .

\sqrt[115]{\sqrt[50]{{({0.5}^{80})}^{50}}}

$\sqrt[115]{\sqrt[50]{{({0.5}^{80})}^{50}}}$

Step 4

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

\sqrt[115]{{0.5}^{80}}

$\sqrt[115]{{0.5}^{80}}$

Step 5

Raise

0.5

$0.5$ to the power of

80

$80$ .

\sqrt[115]{0}

$\sqrt[115]{0}$

Step 6

The result can be shown in multiple forms.

Exact Form:

\sqrt[115]{0}

$\sqrt[115]{0}$

Decimal Form:

0.61743027 \dots

$0.61743027 \dots$