What is (sqrt(2x^{17)+x^{-1}})^n ?

The solution to (sqrt(2x^{17)+x^{-1}})^n is (2x^{17}+1/x)^{n/2}

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simplify (sqrt(2x^{17)+x^{-1}})^n

simplify

(2 x^{17} + x^{- 1})^{n}

(2 x^{17} + \frac{1}{x})^{\frac{n}{2}}

Solution steps

(2 x^{17} + x^{- 1})^{n}

Apply radical rule:

a = a^{\frac{1}{2}}

= ((2 x^{17} + x^{- 1})^{\frac{1}{2}})^{n}

Apply exponent rule:

(a^{b})^{c} = a^{b c},

assuming

a \geq 0

= (2 x^{17} + x^{- 1})^{\frac{1}{2} n}

Simplify

\frac{1}{2} n : \frac{n}{2}

= (2 x^{17} + x^{- 1})^{\frac{n}{2}}

Apply exponent rule:

a^{- 1} = \frac{1}{a}

= (2 x^{17} + \frac{1}{x})^{\frac{n}{2}}

0.36 \cdot 1 0^{- 18}

2.5 \cdot (10 \cdot 1 0^{- 3})

44 e n t r e^{499468}

4 - x \cdot 2 x - 6

(3 \cdot 1 0^{9}) (2 \cdot 1 0^{9})

What is (sqrt(2x^{17)+x^{-1}})^n ?
The solution to (sqrt(2x^{17)+x^{-1}})^n is (2x^{17}+1/x)^{n/2}