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rosijanka [135]
3 years ago
11

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

Mathematics
1 answer:
Alik [6]3 years ago
6 0

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

a^{-m}=\dfrac{1}{a^m}=\left(\dfrac{1}{a}\right)^m

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

2^{-\frac{1}{2}}=\dfrac{1}{2^\frac{1}{2}}=\left(\dfrac{1}{2}\right)^{\frac{1}{2}}

which is the right hand side.

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