Linear Algebra Examples

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

Step 1

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

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

Step 2

Rewrite ${0.5}^{4000}$ as ${({0.5}^{80})}^{50}$ .

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

Step 3

Rewrite $\sqrt[5750]{{({0.5}^{80})}^{50}}$ as $\sqrt[115]{\sqrt[50]{{({0.5}^{80})}^{50}}}$ .

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

Step 4

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

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

Step 5

Raise $0.5$ to the power of $80$ .

$\sqrt[115]{0}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\sqrt[115]{0}$

Decimal Form:

$0.61743027 \dots$