${[2^{- 1} + 3^{- 1} + 4^{- 1}]}^{0} =______$ . Fill in the blank to make the statement true.

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Solution

Using the law of exponent, $a^{0} = 1$ :
An exponent of a number represents the number of times the number is multiplied by itself.
The rules of exponents are:
$a^{m} \times a^{n} = a^{m + n}$
$\frac{a^{m}}{a^{n}} = a^{m - n}$
${(a^{m})}^{n} = a^{m n}$
$\frac{a^{n}}{b^{n}} = {(\frac{a}{b})}^{n}$
$a^{0} = 1$
$a^{- m} = \frac{1}{a^{m}}$
Therefore, ${[2^{- 1} + 3^{- 1} + 4^{- 1}]}^{0} = 1$
Hence, the answer to the given question is $1$ .

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