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

The reason is that, the square root of any real number, cannot be negative in real number system.

Step-by-step explanation:

Rational exponents often referred to as fractional exponent is a mathematical terms that describes the interger exponent and its nth root, such that the interger is used as the numerator, which will be the power of denominator, while the denominator is the root of the interger.

Therefore, given the denominator to be positive even, then the nth root, will be even root such as square root, 4th root, 6th root, 8th root etc.

However, if the denominator is negative number, this implies that, we are finding for even root, of a negative number, which is technically impossible nor defined, because a negative times a negative is a positive, as is a positive times a positive, so there is no way to multiply the same number twice and get a negative.

For example: there is no square roots of (-16), since -4 x -4 = + 16 and +4 x +4 = +16

Hence, the nth root of a negative number does not exist in real number system.

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1

1. 34

2. 268

3. x=14.4

step-by-step explanation: