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Airida [17]
3 years ago
11

Explain why rational exponenets are not defined when the denominator of the exponent in lowest terms is even and the base is neg

ative. << Read Less
Mathematics
1 answer:
dolphi86 [110]3 years ago
8 0
Recall that one of the rules of exponents states that
x^{ \frac{m}{n} }= \left(\sqrt[n]{x} \right)^m

Now, let x be a negative number and n, an even number, then
(-x)^{ \frac{m}{n} }= \left(\sqrt[n]{(-x)} \right)^m

But the even root of a negative number is not a real number.
for example, \sqrt{-1} is not a real number, rather a complex number.

Hence, <span>rational exponents are not defined when the denominator of the exponent in lowest terms is even and the base is negative.</span>
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