chuctran6805 chuctran6805
  • 21-10-2019
  • Mathematics
contestada

Show why the following statement is true:
2^−1/2 = 1/2^1/2

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Аноним Аноним
  • 21-10-2019

In order to solve a negative exponent, you have to consider the multiplicative inverse of the base:

[tex]a^{-m}=\dfrac{1}{a^m}=\left(\dfrac{1}{a}\right)^m[/tex]

So, if we solve the negative exponent on the left hand side, we have

[tex]2^{-\frac{1}{2}}=\dfrac{1}{2^\frac{1}{2}}=\left(\dfrac{1}{2}\right)^{\frac{1}{2}}[/tex]

which is the right hand side.

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