Solve sqrt{17}div1/(sqrt{17)^5}div(sqrt{17})^4

$$\sqrt { 17 } \div \frac { 1 } { ( \sqrt { 17 } ) ^ { 5 } } \div ( \sqrt { 17 } ) ^ { 4 }$$

Evaluate

$$17$$

Solution Steps

Divide \sqrt{17} by \frac{1}{\left(\sqrt{17}\right)^{5}} by multiplying \sqrt{17} by the reciprocal of \frac{1}{\left(\sqrt{17}\right)^{5}}.

$$\frac{\sqrt{17}\left(\sqrt{17}\right)^{5}}{\left(\sqrt{17}\right)^{4}}$$

To multiply powers of the same base, add their exponents. Add 1 and 5 to get 6.

$$\frac{\left(\sqrt{17}\right)^{6}}{\left(\sqrt{17}\right)^{4}}$$

Cancel out \left(\sqrt{17}\right)^{4} in both numerator and denominator.

$$\left(\sqrt{17}\right)^{2}$$

The square of \sqrt{17} is 17.

$$17$$

Factor

$$17$$